Rotating black holes with strong magnetic fields lead to an outward energy flux in the form of jets governed by the Blandford-Znajek mechanism. These jets depend on factors such as accretion rate, magnetic flux and the spin of the black hole. When such rotating black holes get attached to a cosmic string, it leads to a further rotational energy extraction, leading to a reduced spin. We consider such a system and investigate the effect this reduced spin has on the jet power and its dependence on the cosmic string tension, $\mu$. It is shown that for a constant magnetic flux and accretion rate, the jet energy flux is inversely proportional to $\mu^2$. Interestingly, the rate of this energy flux varies with time and is again dependent on $\mu$. We also study the total angular momentum evolution of the black hole by considering four major effects: accretion, jets, cosmic string energy extraction and the Bardeen-Petterson effect. Further, we attempt to analyse the condition for the spin-down of a black hole due to these effects and find out that it is possible for both small and large string tensions, with a higher possibility for larger string tensions. Another interesting phenomenon that has been proposed is the alignment of the jet with the cosmic string. Additionally, the Bardeen-Petterson effect also leads to alignment or misalignment of the inner and outer disks depending on the alignment of the string. In this manuscript we propose that these results might have an observable effect and hence could serve as a potential detection method for cosmic strings.

We study the prospects of the Lunar Gravitational-Wave Antenna (LGWA), a proposed deci-Hz GW detector, to observe binary black holes (BBHs) and enable multiband science with ground-based detectors. We assess the detectability of the events observed by current instruments up to the GWTC-4.0 data release, and of simulated populations consistent with the latest reconstruction by the LIGO-Virgo-KAGRA Collaboration. We find that LGWA alone would have been able to observe more than one third of the events detected so far, and that it could detect $\sim\!90$ events merging in the ground-based band per year out to redshifts $z\sim3-5$. Current detectors at design sensitivity and 100% duty cycle could detect thousands of BBHs per year, with one to a few hundred multiband counterparts in LGWA. Third-generation (3G) detectors can observe most of the BBHs detected by LGWA merging in their frequency band in the simulated mass range $7\,{\rm M}_\odot\lesssim M_{\rm tot}\lesssim 600\,{\rm M}_\odot$, enabling systematic joint analyses of hundreds of events. The short time to merger from the deci-Hz band to the Hz-kHz band (typically months to a year) allows for early warning, targeted follow-up, and archival searches. Multiband observations of intermediate-mass BBHs in the deci-Hz band are particularly promising. We perform an injection study for a GW231123-like system (the most massive BBH detection to date, which accumulates $\sim 10^5$ inspiral cycles in LGWA) and show that deci-Hz observations can measure the chirp mass even better than 3G instruments and yield good sky localization and inclination measurement, even with a single observatory. Opening the deci-Hz band would substantially improve the prospects of GW astronomy for intermediate-mass BBHs.

Recent work has highlighted the importance of a fully relativistic treatment of the dephasing of gravitational waves induced by dark-matter overdensities in extreme mass-ratio inspirals (EMRIs). However, a general-relativistic description of the dark matter phase-space distribution is currently available only for the case of a dark matter "spike" arising from adiabatic black hole growth. Here we develop a fully general-relativistic formalism for the more realistic scenario in which a supermassive stellar progenitor collapses to a black hole and produces a shallower dark matter overdensity, or "mound". We follow self-consistently the evolution of the supermassive star, its collapse, and the subsequent growth of the resulting black hole, together with the collisionless dark matter orbits. We find that in the regime where the collapse becomes non-adiabatic, the dark matter distribution function is significantly reshaped, with a clear depletion in the low-binding-energy region of phase space. Our results provide a more realistic prediction for the dark matter phase-space distribution around supermassive black holes, which is an essential step in our programme to use future EMRI observations to extract information about both the nature of dark matter and the formation history of the black hole.

An extremal Reissner-Nordström black hole can form in finite time in the gravitational collapse of a massless charged scalar field. The proof of this is based on the method of characteristic gluing, which involves making an Ansatz for the scalar field at the horizon. We perform a numerical investigation of the characteristic gluing procedure for several different Ansätze. In each case, gluing is possible only if the final black hole mass is large enough. We find that the minimum required mass varies significantly for different Ansätze. We also consider the effect of including a mass term for the scalar field. In this case, for each Ansatz we determine the maximum mass-to-charge ratio for the scalar field such that gluing is possible. Analogous results are obtained for a non-zero cosmological constant.

We construct solitonic Hayward-boson stars (SHBSs) in Anti-de Sitter (AdS) spacetime, which consists of the Einstein-Hayward model and a complex scalar field with a soliton potential. Our results reveal a critical magnetic charge $q_c$. For $q\geq q_c$ in the limit of $\omega \rightarrow 0$, the matter field is primarily distributed within the critical radius $r_c$, beyond which it decays rapidly, while the metric components $-g_{tt}$ and $1/g_{rr}$ become very small at $r_c$. These solutions are termed ``frozen solitonic Hayward-boson stars" (FSHBSs). Continuously decreasing $\Lambda$ disrupts the frozen state. However, we did not find a frozen solution when $q

We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing vector field. If the dominant energy condition is satisfied for null vectors, it follows that an extension of the near-horizon geometry admits an enhanced isometry group containing $SO(2,1)$ or the 2D Poincaré group $\mathbb{R}^2 \rtimes SO(1,1)$. In the latter case, the associated Aretakis instability for a massless scalar field is shifted by one order in the derivatives of the field transverse to the horizon. We consider a broad class of examples including Einstein-Maxwell(-Chern-Simons) theory and Yang-Mills theory coupled to charged matter. In these examples we show that the symmetries are inherited by the matter fields.

We revisit Yeom's annihilation-to-nothing scenario using a modified Wheeler-DeWitt (WDW) equation, incorporating higher curvature corrections. By taking these corrections into account, we show that singularity resolution does not occur within low-energy effective field theory (EFT). Since general relativity (GR) is itself only a low-energy EFT of an underlying ultraviolet (UV) theory, it is unlikely that true singularity resolution can emerge within its domain of validity. Our analysis does not contradict Yeom's conjecture but clarifies that any true resolution of the black hole singularity necessarily requires the inclusion of UV degrees of freedom beyond the scope of GR.

The final equilibrium stage of stellar evolution can result in either a black hole or a compact object such as a white dwarf or neutron star. In general relativity, both stationary black holes and stationary stellar configurations are known to be axisymmetric, and black hole rigidity has been extended to several higher curvature modifications of gravity. In contrast, no comparable result had previously been established for stationary stars beyond general relativity. In this work we extend the stellar axisymmetry theorem to a broad class of diffeomorphism invariant metric theories. Assuming asymptotic flatness and standard smoothness requirements, we show that the Killing symmetry implied by thermodynamic equilibrium inside the star uniquely extends to the exterior region, thereby enforcing rotational invariance. This demonstrates that axisymmetry of stationary stellar configurations is not a feature peculiar to Einstein gravity but a universal property of generally covariant gravitational theories, persisting even in the presence of higher curvature corrections.

Nonlocal modifications of gravity derive from corrections to the quantum gravitational stress tensor which grow nonperturbatively strong during primordial inflation and may persist to the current epoch. Phenomenological constructions have been given that realize MOND in gravitationally bound systems and, separately, reproduce all the cosmological phenomena usually ascribed to dark matter, including the cosmic microwave background radiation, baryon acoustic oscillations and linearized structure formation. In this work we exhibit a single model that interpolates between the two regimes.

Spacetimes with an ergoregion that is not connected to a horizon are linearly unstable. While the linear regime has been studied in a number of settings, little is known about the nonlinear evolution of this ergoregion instability. Here, we investigate this by numerically evolving the unstable growth of a massless vector field in a rapidly spinning boson star in full general relativity. We find that the backreaction of the instability causes the star to become more gravitationally bound, accelerating the growth, and eventually leading to black hole formation. During the nonlinear growth phase, small scale features develop in the unstable mode and emitted radiation as nonlinear gravitational interactions mediate a direct turbulent cascade. The gravitational wave signal exhibits bursts, akin to so-called gravitational wave echoes, with increasing amplitude towards black hole formation.

We analyze a cosmological solution to the field equations of a modified gravity model where curvature and matter are nonminimally coupled. The current Universe's accelerated expansion is driven by a cosmological constant while the impact of the nonminimal coupling on the expansion history is recast as an effective equation of state for evolving dark energy. The model is analyzed under a tracking solution that follows the minimum of the effective potential for a scalar field that captures the modified theory's effects. We determine the conditions for the existence of this minimum and for the validity of the tracking solution. Cosmological constraints on the parameters of the model are obtained by resorting to recent outcomes of data from the DESI collaboration in combination with the Pantheon+ and Dark Energy Survey supernovae compilations, which give compatible results that point to the presence of a dynamical behavior for dark energy. The gravity model violates the equivalence principle since it gives rise to a fifth force that implies the Earth and Moon fall differently towards the Sun. The cosmological constraints are intersected with limits resulting from a test of the equivalence principle in the Earth-Moon system based on lunar laser ranging data. We find that a variety of model parameters are consistent with both of these constraints, all while producing a dynamical evolution of dark energy with similarities to that found in recent DESI results.

Observing gravitational waves from sub-solar-mass, inspiraling compact binaries would provide almost smoking-gun evidence for primordial black holes. Here, we develop a method to search for ultra-compact binaries with chirp masses ranging from $[10^{-2},10^{-1}]M_\odot$. This mass range represents a previously unexplored gap in gravitational-wave searches for compact binaries: it was thought that the signals would too long for matched-filtering analyses but too short for time-frequency pattern-recognition techniques. Despite this, we show that a pattern-recognition technique, the Generalized frequency-Hough (GFH), can be employed with particular modifications that allow us to handle rapidly spinning-up binaries and to increase the statistical robustness of our method, and call this improved method BinaryGFH-v2. We then design a hypothetical search for binaries in this mass regime, compare the empirical and theoretical sensitivities of this method, and project constraints on formation rate densities and the fraction of dark matter that primordial black holes could compose in both current- and future-generation gravitational-wave detectors. Our results show that our method can be used to search for sub-solar-mass, ultra-compact objects in a mass regime that remains to-date unconstrained with gravitational waves.

The analysis examines how neutrinos behave when their trajectories unfold around a black hole sourced by a Kalb-Ramond field, where spontaneous Lorentz symmetry breaking reshapes the surrounding geometry. Instead of following the conventional order, the study focuses first on the observable consequences: alterations in the neutrino-antineutrino annihilation energy output, shifts in the oscillation phase accumulated along the path, and distortions in flavor conversion probabilities induced by gravitational lensing. These features are then tied to the Lorentz-violating spacetime structure, which governs the propagation of the neutrinos. Numerical simulations are carried out for both two- and three-flavor descriptions, with normal and inverted mass orderings.

The astrophysical foreground from compact-binary coalescence signals is expected to be a dominant part of total gravitational wave (GW) energy density in the frequency band of the third-generation detectors. The detection of any other subdominant stochastic GW background (GWB), especially a primordial GWB, will be disturbed by the astrophysical foreground, which needs to be cleaned for further studies of other stochastic GWB. Although previous studies have proposed several cleaning methods, the foreground from subthreshold binary neutron stars (BNS) has been a major obstacle to remove. In this paper, we propose the novel idea to acquire better estimation of the unresolved foreground, by using the information about its anisotropies. We simulate the BNS population and compute its angular power spectrum and shot noise. We find that the shot noise from BNS is too faint to observe after subtracting loud signals due to the limited angular resolution of the third-generation detectors. This justifies the approximation regarding the unresolved foreground as an isotropic component. We also discuss the angular resolution necessary to make our method valid for the foreground subtraction.

Recent efforts have shown that Kantowski-Sachs spacetime provides a useful framework for analyzing perturbations inside a Schwarzschild black hole (BH). In these studies, the adoption of a Hamiltonian formulation offers an insightful perspective. The aim of this work is twofold. First, we revisit and elaborate the results obtained so far in Kantowski-Sachs, with the focus placed on axial perturbations. In particular, by exploiting the relation between this spacetime and the interior of a nonrotating BH, we consider the extension of those results to the exterior geometry of the BH. In this way, we clarify the relation between the axial perturbative gauge invariants emerging from the canonical analysis and the already well-established axial BH invariants, often referred to as master functions. We do so by providing a unified picture of the Hamiltonian formalism, which does not distinguish, formally, between exterior and interior geometries. The second objective is to explore the role of Darboux transformations, which were found as hidden symmetries in the context of BH perturbations, and their appearance in the Hamiltonian setting. Within this framework, the Hamiltonian formulation provides a clear geometric interpretation and characterization of Darboux transformations within the axial sector, viewing them as the set of canonical transformations between Hamiltonians for axial master functions.

Master functions of black holes are fundamental tools in gravitational-wave physics and are typically derived within a Lagrangian framework. Starting from the Kantowski-Sachs geometry, one can instead construct a perturbative Hamiltonian description for the interior region of an uncharged and nonrotating black hole. This approach provides a complementary perspective and enables a quantum treatment of the background geometry and its perturbations. In this work, we extend the application of this formulation to the exterior region and establish a correspondence between the perturbative invariants of the canonical approach and the master functions commonly used in black hole analyses. Once a consistent Hamiltonian description for their canonical counterparts is obtained, a hybrid quantization of the master functions follows naturally.

In a previous paper [9], we proved the following singularity theorem applicable to cosmological models with a positive cosmological constant: if a four-dimensional spacetime satisfying the null energy condition contains a compact Cauchy surface which is expanding in all directions, then the spacetime is past null geodesically incomplete unless the Cauchy surface is topologically a spherical space. The proof in [9] made use of the positive resolution of the surface subgroup conjecture [15]. In this note, we demonstrate how the less-broadly-known positive resolution of the virtual positive first Betti number conjecture [1] provides a more streamlined and unified approach to the proof. We illustrate the theorem with some examples and analyze its rigidity under null geodesic completeness.

We study the backreaction of quantum fields in the Boulware vacuum state on the Schwarzschild geometry, using the Riegert--Mottola--Vaulin renormalized stress-energy tensor derived from the conformal anomaly. An order-reduction procedure is applied to the first order, paying special attention to the conservation of the resulting stress-energy tensor. The results obtained in these different situations are compared between them, and also to recent works in the literature using other approximations for the renormalized stress-energy tensor.

In recent years, pulsar timing arrays (PTAs) have reported evidence for a nanohertz gravitational-wave (GW) background. As radio telescope sensitivity improves, PTAs are also expected to detect continuous gravitational waves from individual supermassive black hole binaries. Nanohertz GWs generate both Earth and pulsar terms in the timing data, and the time delay between the two terms encodes the pulsar distance. Precise pulsar distance measurements are critical to fully exploiting pulsar-term information, which can improve the measurement precision of GW sources' sky position parameters and thus enhance the GW sky-localization capability. In this work, we propose a new pulsar distance estimation method by using pulsar-term phase information from GWs. We construct two-dimensional distance posteriors for pulsar pairs based on the simulated GW signals and combine them to constrain individual pulsar distances. Compared with the existing one-dimensional method, our approach reduces the impact of source-parameter uncertainties on pulsar distance measurements. Considering four GW sources and a PTA of 20 pulsars with a white-noise level of 20 ns, we find that a significant fraction of pulsars at distances $\lesssim 1.4$ kpc can achieve sub-parsec distance precision over a 15-year observation.

The neutron star -- black hole (NSBH) binary GW200105 was recently found to have significant residual orbital eccentricity at a gravitational-wave frequency of 20 Hz~\cite{Morras:2025xfu}. The event was originally identified with moderate significance by matched-filter searches that employ non-eccentric templates. The neglect of relevant physical effects, such as orbital eccentricity, can severely reduce the sensitivity of the search and, consequently, also the significance of an event candidate. Here, we present a targeted eccentric search for GW200105. The eccentric search identifies GW200105 as the most significant event with a signal-to-noise ratio of $13.4$ and a false alarm rate of less than 1 in 1000 years. The best-matching template parameters are consistent with the Bayesian inference result, supporting the interpretation of GW200105 as an NSBH that formed through dynamical mechanisms and not isolated binary evolution.

In this work, we will explore the effects of F(R) theories in the classical scheme using the anisotropic Bianchi Type I cosmological model with standard matter employing a barotropic fluid with equation of state $P=\gamma \rho$. In this work we present the classical solutions in two gauge, N=1 and $N=6ABCD=6\eta^3D$ obtaining some results that are usually used as ansatz to solve the Einstein field equation. For completeness, we present the solutions in vacuum as well.

Gravitational-wave observations of extreme mass-ratio inspirals (EMRIs) in vacuum are largely insensitive to the internal structure of the small compact companion. We show that this conclusion can change when the central black hole is surrounded by a dense dark matter environment. We compute, for the first time, the relativistic dynamical-friction force on a neutron star moving through a collisionless medium and its impact on the evolution of EMRIs embedded in dense dark matter spikes. We then perform a Bayesian parameter-estimation analysis of simulated LISA observations to assess the measurability of both spike properties and the companion's internal structure. We find that, in our fiducial dark matter spike models, EMRIs with signal-to-noise ratio (SNR) $\gtrsim 20$ already allow us to distinguish neutron star from black hole companions, while events with SNR $\gtrsim 400$ make it possible to discriminate between different neutron star equations of state.

We study the quantum version of the classical twin paradox in special relativity by replacing the twins with quantum detectors, and studying the transitions and entanglement induced by coupling them to a quantum field. We show that the \textit{changes} in direction of acceleration leave imprints on detector responses and entanglement, inducing novel features which might have relevance in black hole spacetimes.

The Sachdev-Ye-Kitaev (SYK) model has attracted widespread attention due to its relevance to diverse areas of physics, such as high temperature superconductivity, black holes, and quantum chaos. The model is, however, extremely challenging to realize experimentally. In this work, we show how a particular form of Floquet engineering, termed ``kinetic driving'', effectively eliminates single-particle processes and creates quasi-random all-to-all interactions when applied to models of Hubbard type. For the specific case of the Bose-Hubbard model, we explicitly verify that the driven system indeed reproduces SYK physics by direct comparison of the spectral form factor and out-of-time ordered correlation functions (OTOCs). Our findings indicate that a cold-atom realization of kinetic driving -- achieved through modulation of hopping amplitudes in an optical lattice -- offers a practical and accurate platform for quantum simulation of the SYK model.

What does ``Big Bang'' actually mean? What was the origin of these two words? It has often been said that the expression ``Big Bang'' began as an insult. Even if this were true, it would be just an irrelevant part of the whole issue. There are many more aspects hidden under this name, and which are seldom explained. They will be discussed in this work. In order to frame the analysis, help will be sought from the highly authoritative voices of two exceptional writers: William Shakespeare and Umberto Eco. Both Shakespeare and Eco have explored the tension existing between words and the realities they name. With the conclusion that names are, in general, just labels, simple stickers put to identify things. And this includes those given to great theorems or spectacular discoveries. Not even ``Pythagoras' theorem'' was discovered by Pythagoras, as is now well-known. Stigler's law of eponymy is recalled to further substantiate those statements. These points will be at the heart of the investigation carried out here, concerning the very important concept of ``Big Bang''. Everybody thinks to know what ``the Big Bang'' is, but only very few do know it, in fact. When Fred Hoyle first pronounced these two words together, on a BBC radio program, listeners were actually left with the false image that Hoyle was trying to destroy. That is, the tremendous explosion of Lemaître's primeval atom (or cosmic egg), which scattered all its enormous matter and energy content throughout the rest of the Universe. This image is absolutely wrong! As will be concluded, today the label ``Big Bang'' is used in several different contexts: (a) the Big Bang Singularity; (b) as the equivalent of cosmic inflation; (c) speaking of the Big Bang cosmological model; (d) to name a very popular TV program; and more.

Recent observations of high redshift galaxies by the James Webb Space Telescope suggest the presence of a bright population of galaxies that is more abundant than predicted by most galaxy formation models. These observations have led to a rethinking of these models, and numerous astrophysical and cosmological solutions have been proposed, including cosmic strings, topological defects that may be remnants of a specific phase transition in the very early moments of the Universe. In this paper, we integrate cosmic strings, a source of nonlinear and non-Gaussian perturbations, into the semi analytical code Zeus21, allowing us to efficiently predict the ultraviolet luminosity function (UVLF). We conduct a precise study of parameter degeneracies between star-formation astrophysics and cosmic-string phenomenology. Our results suggest that cosmic strings can boost the early-galaxy abundance enough to explain the measured UVLFs from the James Webb and Hubble Space Telescopes from redshift z = 4 to z = 17 without modifying the star-formation physics. In addition, we set a new upper bound on the string tension of $G\mu \lessapprox 10^{-8}$ ($95\%$ credibility), improving upon previous limits from the cosmic microwave background. Although with current data there is some level of model and prior dependence to this limit, it suggests that UVLFs are a promising avenue for future observational constraints on cosmic-string physics.

We analyze entanglement generated by the Schwinger effect using a mode-by-mode formalism for scalar and spinor QED in constant backgrounds. Starting from thermal initial states, we derive compact, closed-form results for bipartite entanglement between particle-antiparticle partners in terms of the Bogoliubov coefficients. For bosons, thermal fluctuations enhance production but suppress quantum correlations: the logarithmic negativity is nonzero only below a (mode-dependent) critical temperature $T_c$. At fixed $T$, entanglement appears only above a critical field $E_{\text{crit,entang}}$. For fermions, we observe a qualitatively different pattern: at finite $T$ entanglement exists only within a finite window $E_{\text{min}} < E < E_{\text{max}}$, with a temperature-independent optimal field strength $E_{*}$ that maximizes the logarithmic negativity. Entanglement is vanishing above $T_{\text{max}}=\omega/\text{arcsinh}(1)$. We give quantitative estimates for analog experiments, where our entanglement criteria convert directly into concrete temperature and electric field constraints. These findings identify realistic regimes where the quantum character of Schwinger physics may be tested in the laboratory.

Cosmological perturbations generated during inflation exhibit striking quantum features, including entanglement and high circuit complexity. Yet their observational signatures remain effectively indistinguishable from classical stochastic variables. We quantify this tension by showing that quantum inflationary perturbations are continuous variable stabilizer states with vanishing quantum magic, a necessary resource for universal quantum computation as measured by Wigner negativity. Consequently, despite their quantum origins and description, these states can be efficiently simulated using classical algorithms. We further show that the Wigner negativity arising from primordial non-Gaussianity is suppressed not only by the non-linearity parameter $f_{NL}$, but also by the exponential squeezing of the perturbations. Viewing the early universe as a "high complexity, low magic" regime provides another perspective of what it means for the origin of structure in the universe to be "quantum."

In 2507.17558, we provide a map from a scalar theory on $(D+2)$-dimensional Minkowski spacetime to a scalar theory with a continuous mass spectrum on $(D+1)$-dimensional de Sitter spacetime, and propose a link between celestial amplitudes and cosmological correlators (the cosmological-celestial dictionary). We extend the construction to fields with spin 1 and 2, and find that massless spin fields map to spin fields with continuous mass spectra. In this construction, we identify the de Sitter counterparts of the Nambu-Goldstone modes associated with the asymptotic symmetries in Minkowski spacetime. For $U(1)$ gauge theories, the counterpart is restricted to the massless sector within the continuous Proca spectrum, while for linearized gravity supertranslations are encoded in the partially massless sector and superrotations in the strictly massless sector. Using the identification, we reveal that the associated Ward-Takahashi identities of the cosmological correlators reproduce the conformally soft photon and graviton theorems via the cosmological-celestial dictionary. In particular, the celestial stress tensor is derived from the asymptotic limit of gravitons in de Sitter spacetime.

This work explores the possibility that five-dimensional primordial rotating black holes could account for all, or a significant portion, of the dark matter in our universe. Our analysis is performed within the context of the ``dark dimension'' scenario, a theoretical consequence of the Swampland Program that predicts a single micron-scale extra dimension to explain the observed value of dark energy. We demonstrate that within this scenario, the mass loss of a primordial rotating black hole sensitive to the fifth dimension is significantly slower than that of its four-dimensional counterpart. Consequently, primordial black holes with an initial mass of $M\gtrsim 10^{10}$g can survive to the present day and potentially constitute the dominant form of dark matter. Finally, we investigate the memory burden effect and find that it dramatically prolongs the lifetime of five-dimensional rotating primordial black holes, making them compelling candidates for all the dark matter in the universe.

We show that the quantum-mechanical probability distribution involving complex probability amplitudes can be derived from three natural conditions imposed on a relativistically invariant probability function describing the motion of a particle that can take multiple paths simultaneously. The conditions are: (i) pairwise Kolmogorov additivity, (ii) time symmetry, and (iii) Bayes' rule. The resulting solution, parameterized by a single constant, is the squared modulus of a sum of complex exponentials of the relativistic action, thereby recovering the Feynman path-integral formulation of quantum mechanics.

We explore a continuum theory of multicritical dynamical triangulations and causal dynamical triangulations in two-dimensional quantum gravity from the perspective of the Chekhov-Eynard-Orantin topological recursion. The former model lacks a causal time direction and is governed by the two-reduced $W^{(3)}$ algebra, whereas the latter model possesses a causal time direction and is governed by the full $W^{(3)}$ algebra. We show that the topological recursion solves the Schwinger-Dyson equations for both models, and we explicitly compute several amplitudes.

We investigate whether the recent DESI DR2 measurements provide or not evidences for dynamical dark energy by exploring the $\omega_0\omega_a$CDM model and its extensions with free $\sum m_{\nu}$ and $N_{\mathrm{eff}}$. Using a comprehensive MCMC analysis with a wide range of cosmological datasets including DESI~DR2 BAO and Ly$\alpha$ data, CMB compressed likelihoods, BBN, cosmic chronometers, and multiple Type~Ia supernova compilations, we assess the statistical preference for departures from $\Lambda$CDM.

The discovery of joint sources of high-energy neutrinos and gravitational waves has been a primary target for the LIGO, Virgo, KAGRA, and IceCube observatories. The joint detection of high-energy neutrinos and gravitational waves would provide insight into cosmic processes, such as progenitor dynamics and outflows. The joint detection of multiple cosmic messengers can also elevate the significance of the observation when some or all of the constituent messengers are sub-threshold, not significant enough to declare their detection individually. Leveraging data from the LIGO, Virgo, and IceCube observatories, we conducted an archival investigation of sub-threshold multimessenger events. Complementing previous analyses, we used minimal assumptions to search for common sources of sub-threshold gravitational-wave and high-energy neutrino candidates during the third observing run (O3) of the Advanced LIGO and Advanced Virgo detectors. Our search did not identify significant joint sources. We therefore derive constraints on the rate density of joint sources for each compact binary merger population as a function of the energy emitted in neutrinos. Only a fraction of the gravitational-wave sources emit neutrinos, if the neutrino emission has high bolometric energy ($>10^{52}$ to $10^{54}$ erg).

In this paper we analyse scalar-tensor theories-specific instances of which include mainstream inflation and dark energy models-in light of the spacetime-matter dichotomy. We argue that it is difficult to categorise the scalar fields as either a pure aspect of the spacetime structure or a pure form of matter, by focusing on the Jordan vs Einstein frames of these theories. We present and evaluate various interpretational options available, concluding that the spacetime-matter dichotomy becomes untenable in this context. At the same time, the ontological and conceptual category of spacetime can be decoupled from that of gravity, with the latter remaining viable in the context of scalar-tensor theories.

In this work, we initiate the study of light-ray operators in four-dimensional de Sitter space focusing on null integrals of the stress tensor. In Minkowski space, the null integral of the stress tensor unifies several ostensibly different constructions, functioning simultaneously as the energy flux operator, the angular contribution to a conserved charge, the averaged null energy operator, and the light transform of the stress tensor. However, we show that the de Sitter analogs of these various interpretations do not necessarily coincide but rather lead to distinct, observer-dependent light-ray operators. We construct four such de Sitter analogs and analyze their matrix elements in a free, conformally coupled scalar theory, showing that they exhibit the expected symmetry and positivity properties.

The effective field theory (EFT) concept provides a necessary tool for obtaining general predictions of low-energy theory valid below its unitarity-breaking scale (cutoff scale). Early Universe inflation and subsequent reheating could be a unique setup for testing potentially observable effects coming from the derivative expansion of the corresponding EFT around the flat space vacuum. In this work, we consider an EFT describing perturbative reheating dominated by the decay of inflaton to photons caused by the dimension-5 operator $\phi F_{\mu\nu} F^{\mu\nu}$. We compute the graviton production during reheating and high frequency gravitational wave signal due to the bremsstrahlung effect in the presence of $R_{\mu\nu\lambda\rho}F^{\mu\nu} F^{\lambda\rho}$ operator. It may lead to the dominant contribution at high momenta if the EFT cutoff is lower than the Planck mass. Assuming the general consequences of the unitarity and causality constraints, which imply that all EFT operators should be present, and be suppressed by the scales following from the dimension analysis, we obtain the observational constraints (CMB bound for the dark radiation) on the mass of the inflaton and UV cutoff of gravity. We find that for the typical parameters of large field inflation models, the gravitational cutoff scale cannot be lower than $10^{15}$ GeV.

This paper introduces differential-geometric methods to study $n$-dimensional locally conformally flat spaces as submanifolds in $\mathbb{R}^{n+2}$. We derive explicit formulas relating intrinsic and ambient differential-geometric objects, including curvature tensors, the codifferential and laplacian operators. We apply this approach to Friedmann-Lemaître-Robertson-Walker (FLRW) spaces using newfound embedding formulas, obtaining new and simplified expressions for the photon propagator in four dimensions.

We consider correlators smeared against directed wavepackets over a thermal state dual to a single-sided planar AdS black hole. In the large frequency limit, our measurement is simplified using a bulk WKB description. We propose a dictionary that maps the action of smeared boundary operators to flat-space oscillators near an interior bulk point on the thermal state, by analytically continuing late-time operators from the right to the left boundary via an integral transform. Using the dictionary the smeared correlator factorizes to a flat-space like scattering amplitude about the interior event. Our transformed correlators describe local physics in the two-sided black hole interior, while incurring a suppression of $\mathcal{O}(e^{-\beta \omega / 2})$. These measurements necessitate a non-trivial time ordering of operators living on boundary hyperboloids which are causally connected to the past light cone of the bulk point, as well as on a corresponding future branch.

We initiate a systematic study of Einstein-Gauss-Bonnet gravity in the presence of boundaries subject to conformal boundary conditions, in which the conformal class of the boundary metric is kept fixed. In Einstein gravity, the trace of the extrinsic curvature is also fixed at the boundary. Here we generalize this boundary condition with the appropriate higher curvature correction. We study the problem both in Euclidean and Lorentzian signature. In Euclidean signature, we show that, similarly to the Einstein gravity case, the entropy at large temperatures exhibits the behavior of a conformal field theory in one lower dimension. We also show that in the flat space limit, the higher curvature corrections do not contribute to the leading behavior at high temperatures. We conjecture that this result is a universal feature of the flat space limit in the presence of conformal boundaries. We test our conjecture by analyzing charged black holes. In Lorentzian signature, we analyze the dynamics of the boundary Weyl factor in black hole backgrounds at the linearized level.

We present a quasi-local, functional analytic method to locate and invariantly characterize the stationary limit surfaces of black hole spacetimes with stationary regions. The method is based on ellipticity-hyperbolicity transitions of the Dirac, Klein-Gordon, Maxwell, and Fierz-Pauli Hamiltonians defined on spacelike hypersurfaces of such black hole spacetimes, which occur only at the locations of stationary limit surfaces and can be ascertained from the behaviors of the principal symbols of the Hamiltonians. Therefore, since it relates solely to the effects that stationary limit surfaces have on the time evolutions of the corresponding elementary fermions and bosons, this method is profoundly different from the usual detection procedures that employ either scalar polynomial curvature invariants or Cartan invariants, which, in contrast, make use of the local geometries of the underlying black hole spacetimes. As an application, we determine the locations of the stationary limit surfaces of the Kerr-Newman, Schwarzschild-de Sitter, and Taub-NUT black hole spacetimes. Finally, we show that for black hole spacetimes with static regions, our functional analytic method serves as a quasi-local event horizon detector and gives rise to relational concepts of event horizons and black hole entropy.

Between 1972 and 1975, Jacob Bekenstein proposed that black holes possess entropy proportional to their horizon area, and Stephen Hawking derived this relationship from semiclassical quantum field theory in curved spacetime, predicting thermal radiation from black holes. These developments established black hole thermodynamics as a formal framework connecting general relativity, quantum mechanics, and statistical physics. However, this synthesis rests on approximations whose validity remains unproven in regimes where quantum gravitational effects become important. This article provides a detailed overview of the historical development from 1972 to 1975 and surveys modern proposals, such as the holographic principle and gravitational path integrals. We highlight persistent theoretical challenges, including the information paradox, the trans-Planckian problem, backreaction effects, and the absence of experimental verification. The work concludes by identifying which aspects of black hole thermodynamics are well-established and which remain speculative or fundamentally incomplete.

Recent investigations of vacuum polarization in extremely compact stars suggest that, in such regimes, the effective matter content of spacetime may acquire a vacuum-energy equation of state with negative energy density, mimicking a negative cosmological constant. Motivated by this observation, we introduce a general algorithm to modify well-known spherically symmetric regular black hole metrics by replacing their usual de Sitter cores (dSC) with Anti-de Sitter cores (AdSC). Like their dSC counterparts, these AdSC solutions may exhibit two, one, or no horizons depending on the value of a regularization parameter l. We present explicit examples of AdSC-Bardeen and AdSC-Dymnikova metrics, analyze their main properties, and investigate some of their phenomenological signatures using test fields. In particular, we compare their fundamental quasinormal modes and echo signals with those of the dSC cases, highlighting potential avenues for distinguishing them observationally.

Numerical relativity simulations provide a means by which to study the evolution and end point of strong over-densities in cosmological spacetimes. Specific applications include studies of primordial black hole formation and the robustness of inflation. Here we adopt a toy model previously used in asymptotically flat spacetimes to show that, for given values of the over-density and the mean curvature, solutions to the Hamiltonian constraint need not exist, and if they do exist they are not unique. Specifically, pairs of solutions exist on two branches, corresponding to strong-field and weak-field solutions, that join at a maximum beyond which solutions cease to exist. As a result, there is a limit to the extent to which an over-density can be balanced by intrinsic rather than extrinsic curvature on the initial slice. Even below this limit, iterative methods to construct initial data may converge to solutions on either one of the two branches, depending on the starting guess, leading to potentially inconsistent physical results in the evolution.

Laser Interferometer Space Antenna (LISA) observations of massive black hole binaries (MBHBs) will provide long duration inspiral signals with high signal-to-noise ratio (SNR) data, ideal for testing general relativity (GR) in the strong-field and relativistic regime regime. We present an extension of the Flexible Theory-Independent (FTI) framework, adapted to gravitational waves (GWs) from MBHBs observed with LISA, to perform parametrized inspiral tests of GR. This approach introduces generic deviations to the post-Newtonian (PN) coefficients of the frequency-domain GW phase while accounting for the time- and frequency-dependent instrument response, thus effectively identifying potential deviations from GR by constraining modifications to the PN phasing formula. Complementary analyses using Fisher matrix and full Bayesian approaches confirm that LISA observations could improve constraints on agnostic, scale-independent deviations from GR by at least two orders of magnitude compared to the most recent LIGO-Virgo-KAGRA measurements. Since LISA's sensitivity to different GW phases -- inspiral, merger, and ringdown -- varies across the MBHB parameter space with masses between $10^4$ and $10^7M_{\odot}$, the optimal regime for testing agnostic deviations is not known a priori. Our results illustrate how the strength of these constraints depends significantly on both the total mass and the SNR, reflecting the trade-off between inspiral and merger-ringdown contributions to the observed signal. We also investigate the interplay between inspiral-only versus inspiral-merger-ringdown analyses in constraining these inspiral deviation parameters. This work contributes to the development of robust tests of GR with LISA, enhancing our ability to probe the nature of gravity and BHs with GW observations.

In this work, we investigate the cosmological consequences of an effective $f(Q)$ model emerging from the more general $f(Q,T)$ gravity theory under the special equation-of-state condition $\rho + p = 0$. Under this limit, the field equations yield the constraint $F(Q,T)H(t)=C$, implying that the function $F=f_Q$ becomes purely dependent on the nonmetricity scalar $Q$, and the background evolution mimics that of the standard $\Lambda$CDM model. We derive the resulting functional forms of $f(Q)$, obtain the corresponding effective cosmological constant, and analyze the physical nature of this reduction. To test the model against observations, we constrain the parameters $H_0$, $\Omega_m$, and $S_8$ using cosmic chronometers (CC), baryon acoustic oscillations (BAO), and Pantheon+ SN Ia datasets. A comparative analysis is performed using both the conventional Bayesian Markov Chain Monte Carlo (MCMC) sampling and a machine-learning based Artificial Neural Network (ANN) emulator. We find that the ANN approach yields tighter posterior constraints while significantly reducing computational time. The model successfully reproduces the observational trends of each dataset and offers insights into the persistent $H_0$ and $S_8$ tensions. Our results indicate that effective nonmetricity-based dark energy scenarios derived from $f(Q,T)$ gravity provide a viable and observationally consistent alternative to $\Lambda$CDM, with future high-precision surveys expected to further distinguish between these frameworks.

We prove the Angular Momentum Penrose Inequality, a fundamental result connecting the total mass of an isolated gravitational system to the size and spin of any black holes it contains. The inequality states that the mass of a spacetime must be at least as large as a specific combination of the black hole's horizon area and angular momentum, with the bound being tight precisely for the Kerr family of rotating black holes. The proof combines four techniques: solving a geometric equation that straightens out the initial data, applying a conformal transformation that encodes angular momentum, tracking how angular momentum is preserved through the construction, and invoking known bounds that prevent black holes from spinning too fast. A central innovation is a new notion of mass that incorporates both the standard Hawking mass and angular momentum, and which increases monotonically along a natural geometric flow from the black hole horizon out to infinity. As an application, we also prove the Charged Penrose Inequality for non-rotating charged black holes, showing that electric charge contributes to the mass bound in a manner analogous to angular momentum.

Vortons are of interest in high-energy physics as possible dark matter candidates and as probes of Grand Unified Theories. Using the recently derived weak-field metric for a chiral vorton, we study the dynamics of test particles by analyzing both timelike and null geodesics. We identify several classes of trajectories, including bound precessing orbits, circular orbits, toroidal, and crown-type oscillations, as well as unbound scattering paths. Poincare surfaces of section reveal transitions between regular and chaotic motions that depend sensitively on the vorton tension $G\mu$ and initial conditions. We further compute the Lense-Thirring and general spin-precession frequencies for gyroscopes along Killing trajectories. The resulting precession profiles exhibit several distinct features not present in Kerr black holes but reminiscent of Kerr naked singularities, such as: divergences near the ring core, and multi-minima structures. These dynamical and precessional signatures may offer potential observational pathways for detecting vortons.

Measurements of the binary black hole spin distribution from the growing catalog of gravitational-wave observations can help elucidate the astrophysical processes shaping the formation and evolution of these systems. Spin-orbit resonances are one process of interest, in which the component spin vectors and the orbital angular momentum align into a common plane and jointly precess about the total angular momentum of the system. These resonances, which occur preferentially in systems formed via isolated binary evolution with strong tidal effects, lead to excesses in the distribution of the azimuthal angle between the projections of the component spin vectors onto the orbital plane at $\phi_{12}=0,\pm\pi$. In this work, we conduct the first hierarchical analysis modeling the population-level distribution of $\phi_{12}$ simultaneously with the other mass and spin parameters for simulated binary black hole populations to determine whether spin-orbit resonances can be reliably constrained. While we are unlikely to find definitive evidence for spin-orbit resonances with a population of the size expected by the end of the ongoing LIGO-Virgo-KAGRA fourth observing run, we correctly recover the various $\phi_{12}$ distributions we simulate within uncertainties. We find that we can place meaningful constraints on the relative excesses at $\phi_{12}=0,\pm\pi$, which encodes information about binary mass transfer. We can also distinguish between fully isotropic spin angle distributions and those with features in the spin azimuth and tilt distributions. Thus, we show that population-level measurements of the $\phi_{12}$ distribution offer a reliable, novel way to probe binary formation channels, dynamics, and mass transfer with gravitational-wave observations.

The standard paradigm of cosmology assumes two distinct dark components, namely dark matter and dark energy. However, the necessity of splitting the dark-side world into two sectors has not been experimentally or theoretically proven. Unified dark fluid models provide an alternative in which a single fluid accounts for both phenomena. It is shown in Wang et al. 2024 that a PAge-like unified dark fluid (PUDF) can explain both the cosmic microwave background (CMB) and late-universe data, with the fitting quality not much worse than the standard Lambda cold dark matter ($\Lambda$CDM) model. Using the Planck 2018 CMB, baryon acoustic oscillations measurement from the dark energy spectroscopic instrument (DESI) data release 2, dark energy survey 5-year supernova data, and cosmic-chronometer data, we update the constraints on PUDF and clarify its physical implications. We show that PUDF can reproduce the primary CMB anisotropies, the background expansion history, and linear growth that are very close to the $\Lambda$CDM prediction. Nevertheless, the combined datasets still favor $\Lambda$CDM, largely due to the significant tension between CMB and DESI + SNe data, which exceeds the $4\sigma$ level in PUDF and remains non-negligible in the $w$CDM framework. Using mock data generated from the Planck best-fit $\Lambda$CDM model, we find that PUDF and $\Lambda$CDM cannot be statistically distinguished, indicating that the precision of current data is insufficient to separate the two models. Overall, the apparent preference for $\Lambda$CDM may be driven by dataset inconsistencies rather than a genuine physical difference, leaving unified dark fluid models as viable alternatives within current observational limits.

A direct interaction between dark energy and dark matter provides a natural and important extension to the standard $\Lambda$CDM cosmology. We perform a non-parametric reconstruction of the vacuum energy ($w=-1$) interacting with cold dark matter using the cosmological data from DESI DR2, Planck CMB, and three SNIa samples (PP, DESY5, and Union3). By discretizing the coupling function $\beta(z)$ into 20 redshift bins and assuming a Gaussian smoothness prior, we reconstruct $\beta(z)$ without assuming any specific parameterization. The mean reconstructed $\beta(z)$ changes sign during cosmic evolution, indicating an energy transfer from cold dark matter to dark energy at early times and a reverse flow at late times. At high redshifts, $\beta(z)$ shows a $\sim 2\sigma$ deviation from $\Lambda$CDM. At low redshifts, the results depend on the SNIa sample: CMB+DESI and CMB+DESI+PP yield $\beta(z)$ consistent with zero within $2\sigma$, while CMB+DESI+DESY5 and CMB+DESI+Union3 prefer negative $\beta$ at $\sim2\sigma$. Both $\chi^2$ tests and Bayesian analyses favor the $\beta(z)$ model, with CMB+DESI DR2+DESY5 showing the most significant support through the largest improvement in goodness of fit ($\Delta\chi^2_{\rm MAP}=-17.76$) and strongest Bayesian evidence ($\ln\mathcal{B} = 5.98 \pm 0.69$). Principal component analysis reveals that the data effectively constrain three additional degrees of freedom in the $\beta(z)$ model, accounting for most of the improvement in goodness of fit. Our results demonstrate that the dynamical dark energy preference in current data can be equally well explained by such a sign-reversal interacting dark energy, highlighting the need for future observations to break this degeneracy.

We investigate the neutrino and gravitational wave (GW) signals from accretion disks formed during the failed collapse of a rotating massive star (a collapsar). Following black hole formation, a neutrino-cooled, shocked accretion disk forms, which displays non-spherical oscillations for a period of seconds before becoming advective and exploding the star. We compute the neutrino and GW signals (matter quadrupole, frequencies $\lesssim 100$ Hz) from collapsar disks using global axisymmetric, viscous hydrodynamic simulations. The neutrino signal with typical energies of O$(10)$ MeV is maximal during the neutrino-cooled (NDAF) phase that follows shock formation. This phase lasts for a few seconds and is easily detectable within O$(10-100)$ kpc by the IceCube Neutrino Telescope. Additional neutrino signatures from a precursor equatorial shock and by stochastic accretion plumes during the advective phase are detectable within the galaxy. The GW signal during the NDAF phase is detectable in the galaxy by current and next-generation ground-based observatories. The explosion (memory) GW signal is similar to that of standard core-collapse supernovae and can be probed with a deci-Hertz space-based detector. Shock oscillations during the NDAF phase impart time variations with frequency O$(10-100)$ Hz to the neutrino and GW signals, encoding information about the shock dynamics and inner disk. These time variations can be detectable in neutrinos by IceCube within O$(1-10)$ kpc depending on progenitor model, flavor transformation scenario, and detailed properties of the angular momentum transport mechanism.

We compute a gravitational on-shell action of a finite, spherically symmetric causal diamond in $(d+2)$-dimensional Minkowski spacetime, finding it is proportional to the area of the bifurcate horizon $A_{\mathcal{B}}$. We then identify the on-shell action with the saddle point of the Euclidean gravitational path integral, which is naturally interpreted as a partition function. This partition function is thermal with respect to a modular Hamiltonian $K$. Consequently, we determine, from the on-shell action using standard thermodynamic identities, both the mean and variance of the modular Hamiltonian, finding $\langle K \rangle = \langle (\Delta K)^2 \rangle = \frac{A_{\mathcal{B}}}{4 G_N}$. Finally, we show that modular fluctuations give rise to fluctuations in the geometry, and compute the associated phase shift of massless particles traversing the diamond under such fluctuations.

We present realistic eccentricity distributions for extreme mass ratio inspirals (EMRIs) forming via the two-body relaxation channel in nuclear star clusters, tracking their evolution up to the final plunge onto the central Schwarzschild massive black hole (MBH). We find that EMRIs can retain significant eccentricities at plunge, with a distribution peaking at $e_\mathrm{pl} \approx0.2$, and a considerable fraction reaching much higher values. In particular, up to $20\%$ of the forming EMRIs feature $e_\mathrm{pl} > 0.5$ for central MBH masses $M_\bullet$ in the range $10^5 \mathrm{M_\odot} \leq M_\bullet \leq 10^6 \mathrm{M_\odot}$, partially due to EMRIs forming at large semi-major axes and "cliffhanger EMRI", usually neglected in literature. This highlights the importance of accounting for eccentricity in waveform modeling and detection strategies for future space-based gravitational wave observatories such as the upcoming Laser Interferometer Space Antenna (LISA). Furthermore, we find that the numerical fluxes in energy and angular momentum currently implemented in the FastEMRIWaveforms (FEW) package may not adequately sample the full parameter space relevant to low-mass MBHs ($M_\bullet < 10^6 \mathrm{M_\odot}$), potentially limiting its predictive power in that regime. Specifically, for $M_\bullet=10^5 \mathrm{M_\odot}$ we find that about $75\%$ ($50 \%$) of EMRIs at 2 years (6 months) from plunge fall outside the currently available flux parameter space. Our findings motivate the development of extended flux grids and improved interpolation schemes to enable accurate modeling of EMRIs across a broader range of system parameters.

Gravitational-wave detectors can probe the existence of dark matter with exquisite sensitivity. Here, we perform a search for three kinds of dark matter -- dilatons (spin-0), dark photons (spin-1) and tensor bosons (spin-2) -- using three independent methods on the first part of the most recent data from the fourth observing run of LIGO--Virgo--KAGRA. Each form of dark matter could have interacted with different standard-model particles in the instruments, causing unique differential strains on the interferometers. While we do not find any evidence for a signal, we place the most stringent upper limits to-date on each of these models. For scalars with masses between $[4\times 10^{-14},1.5\times 10^{-13}]$ eV that couple to photons or electrons, our constraints improve upon those from the third observing run by one order of magnitude, with the tightest limit of $\sim 10^{-20}\,\text{GeV}^{-1}$ at a mass of $\sim2\times 10^{-13}\text{ eV}$. For vectors with masses between $[7\times 10^{-13},8.47\times 10^{-12}]$ eV that couple to baryons, our constraints supersede those from MICROSCOPE and Eöt-Wash by one to two orders of magnitude, reaching a minimum of $\sim 5\times 10^{-24}$ at a mass of $\sim 10^{-12}$ eV. For tensors with masses of $[4\times 10^{-14},8.47\times 10^{-12}]$ eV (the full mass range analyzed) that couple via a Yukawa interaction, our constraints surpass those from fifth-force experiments by four to five orders of magnitude, achieving a limit as low as $\sim 8\times 10^{-9}$ at $\sim2\times 10^{-13}$ eV. Our results show that gravitational-wave interferometers have become frontiers for new physics and laboratories for direct multi-model dark-matter detection.

Before we discuss the deflection of light in a gravitational field, we give a brief overview of some basic physical formulas on photon properties, generation and propagation. The much debated problems of the redshift and the photon propagation in a gravitational field is then considered and applied to the calculation of the speed of light. Many citations are given in direct quotations to avoid any misunderstandings. If the quotations are in German, an English translation is provided. Based on this speed, calculated and measured results are recalled on the deflection of light, with emphasis on the deflection near the Sun. We conclude that the speed of light and the deflection angle can be determined by energy and momentum conservation principles.

A mechanism of spontaneous decoherence is examined in which the generator of quantum dynamics is replaced by the imaginary-order (which is fundamentally different from real-order fractional calculus) spectral deformation $H^{1+i\beta}$ for a positive self-adjoint Hamiltonian $H$. The deformation modifies dynamical phases through the factor $E^{i\beta}=e^{i\beta\log E}$, whose rapid oscillation suppresses interference between distinct energies. A non-stationary-phase analysis yields quantitative estimates: oscillatory contributions to amplitudes or decoherence functionals decay at least as $\mathcal{O}(1/|\beta|)$. The kinematical structure of quantum mechanics -- the Hilbert-space inner product, projection operators, and the Born rule -- remains unchanged; the modification is entirely dynamical and acts only through spectral phases. Physical motivations for the deformation arise from clock imperfections, renormalization-group and effective-action corrections that introduce logarithmic spectral terms, and semiclassical gravity analyses in which complex actions produce spectral factors of the form $E^{i\beta}$. The mechanism is illustrated in examples relevant to quantum-gravity-inspired quantum mechanics. A detailed related-work analysis contrasts the present mechanism with Milburn-type intrinsic decoherence, Diósi-Penrose gravitational collapse, GRW/CSL models, clock-induced decoherence, and energy-conserving collapse models, as well as environmental frameworks such as Lindblad master equations, Caldeira-Leggett baths, and non-Hermitian Hamiltonian deformations. This positions $H^{1+i\beta}$ dynamics as a compact, testable, and genuinely novel phenomenological encapsulation of logarithmic spectral corrections arising in quantum-gravity- motivated effective theories, while remaining fully compatible with standard quantum kinematics.