This research applies the generalized technique of gravitational decoupling to the Bardeen black hole, producing novel black hole solutions in the context of Rastall theory. We proceed by decomposition of the field equations corresponding to an additional matter source into two sets, for further considerations. The metric functions of the Bardeen black hole are adopted to specify the first set. The second one, which is subject to an extra source, is resolved considering a linear equation of state of matter. Through the integration of the solutions of these sets, we develop two expanded models and conduct an in-depth analysis of their distinct physical characteristics, governed by specific parameters. We investigate thermodynamic quantities like density, anisotropic pressure, energy bounds, asymptotic flatness, and thermodynamical properties like the Hawking temperature, entropy, and specific heat, etc. Both models are asymptotically flat but violate the energy bounds. Furthermore, the density, radial pressure, and Hawking temperature demonstrate consistent and acceptable behavior. Ultimately, the thermodynamic stability is affirmed through the analysis of specific heat and the Hessian matrix.

We investigate a possible resolution of the dark energy problem within a pair-universe framework, in which the Universe emerges as an entangled pair of time-reversed sectors. In this setting, a global zero-energy condition allows vacuum energy contributions from the two sectors to cancel, alleviating the need for extreme fine-tuning. We propose that the observed dark energy does not originate from vacuum fluctuations but instead arises as an effective entanglement energy between the visible universe and its mirror counterpart. Treating the cosmological constant as an integration constant fixed by boundary conditions rather than a fundamental parameter, we show that the cosmological equations can be formulated without explicitly introducing vacuum energy. By imposing physically motivated boundary conditions at the cosmological event horizon, we obtain an integration constant consistent with the observed dark energy density. The parallel mirror world scenario thus provides a unified framework that may simultaneously explain the origins of dark energy and dark matter.

We investigate the steady, axisymmetric, force-free magnetosphere of Kerr-Sen black hole (BH) within the framework of the Einstein-Maxwell-dilaton-axion (EMDA) theory. By perturbatively solving the nonlinear Grad-Shafranov (GS) equation, we determine the magnetic field configuration and quantify the influence of the dilaton parameter $r_2$ on the energy extraction rate and radiative efficiency. Our results show that both the energy extraction power and the radiative efficiency increase with $r_2$, exceeding those of the standard Kerr BH, whereas the extraction efficiency remain consistent with the Kerr case. In addition, we perform $\chi^2$ statistical analysis using observational data from six binary BH systems, which indicates that the Kerr BH currently provides a better fit for bulk Lorentz factors $\Gamma = 2$ and $5$.

We will address the existence of a new symmetry for an imperfect fluid by introducing local four-velocity gauge-like transformations for the case when there is vorticity. A similar tetrad formulation as to the Einstein-Maxwell spacetimes formalism presented in previous manuscripts will be developed in this manuscript for the imperfect fluids. The four-velocity curl and the metric tensor will be invariant under these kind of four-velocity gauge-like local transformations. While the Einstein-Maxwell stress-energy tensor is locally gauge invariant under electromagnetic gauge transformations, the perfect fluid stress-energy tensor will not be invariant under four-velocity gauge-like local transformations. We will dedicate our analysis to the imperfect fluid stress-energy tensor that will be invariant under local four-velocity gauge-like transformations when additional transformations are introduced for several variables included in the stress-energy tensor itself. We will also pay special attention to the construction of a vorticity stress-energy tensor invariant under local four-velocity gauge-like transformations. An application on neutron stars will be developed in order to show the simplifications brought about by these new tetrads.

In this paper, we study the $D\to3$ limit of Gauss-Bonnet gravity with quintessential matter, obtaining exact solutions that extend the BTZ metric through higher-curvature terms and quintessence coupling. The solutions exhibit a single event horizon whose radius decreases with increasing quintessence parameter $\omega_q$, while developing a curvature singularity at the origin for non-vanishing quintessence. The geodesic analysis reveals stable circular photon orbits exist exclusively for phantom-like quintessence ($\omega_q < -1$). Thermodynamically, the system is stable, since the specific heat is positive, and with evaporation it evolves to stable remnants whose characteristic size decreases as $\omega_q$ increases, with complete evaporation prevented by quintessence effects. Furthermore, we find that all physical quantities intrinsically depend on the parameter $\alpha$ of the Gauss-Bonnet this http URL results demonstrate the profound influence of quintessential matter on both geometric and thermodynamic properties of (2+1)-dimensional black holes, offering new perspectives on gravitational theories in lower dimensions and black hole final states.

The non-linearly coupled Einstein-matter field equations predict the existence of shadows with well-defined boundaries around black holes. We prove that, in spherically symmetric hairy black-hole spacetimes whose matter fields satisfy the weak energy condition, the radii of these shadows are bounded from below by the dimensionless relation $r_{\text{sh}}/r_{\text{H}}\geq 3\sqrt{3}/2$, where $r_{\text{H}}$ is the horizon radius of the central hairy black hole. The characteristic shadow of the (bald) Schwarzschild black-hole spacetime saturates the analytically derived lower bound.

Typical gravitational production of relics from amplification of inflationary perturbations assumes Bunch-Davies initial conditions, i.e. a vacuum with initially no particles. In this paper we investigate the impact of non Bunch-Davies initial conditions to the final abundance of relics, with particular attention to the parameter space where the total dark matter abundance is reproduced. We present a general framework for any initial condition, through which we show their non-trivial effect on both spectrum and late-time abundance. We argue that for particles whose source of conformal symmetry breaking comes only from a mass term (spin-1/2 fermions and conformally coupled scalars), the choice of initial conditions has little impact on the mass range relevant to dark matter. For other particles, e.g. the longitudinal mode of spin-1, we see a large deviation from the standard computation. We exemplify and quantify our results with an initial thermal state and a two-stage inflation scenario, highlighting that the total dark matter can be obtained for a wide range of masses.

This work investigates the cosmology of a thick brane within the context of $f(\mathbb{Q})$ gravity, an extension of symmetric teleparallelism. Using a five-dimensional Friedmann-Lemaître-Robertson-Walker metric, we solve the field equations to obtain dynamic solutions for the scale factor. We demonstrate that the effective cosmological constant on the brane naturally emerges as a function of the extra dimension $\Lambda(y)$, being both generated and confined by the curved geometry of the bulk. We analyze two distinct regimes: Randall-Sundrum-type thin brane and thick brane through the Sine-Gordon model. Our model reproduces accelerated expansion solutions without requiring the introduction of a fundamental cosmological constant on the brane, showing that the cosmic acceleration emerges as a consequence of the brane's embedding and the gravitational dynamics in the bulk . The variation of the $c_i$ parameters in symmetric teleparallelism enables different cosmological scenarios, including de Sitter-type expansion, contraction, and oscillatory solutions. The results indicate that the brane's position in the bulk determines its cosmology, providing a geometric explanation for the smallness of the observed cosmological constant.

We consider a metric-affine formulation of Chern-Simons modified gravity in 2 + 1 dimensions. The theory is built requiring projective invariance, and the structure of the equations is analyzed using a decomposition in terms of scalar, vectorial, and purely tensorial objects. This approach allows us to implement a perturbative approach to study the corrections that emerge around a given background solution, for which we consider a BTZ charged, non-rotating metric. We show that conditions on model parameters are necessary to keep perturbations under control, yielding a rotating solution with a constant angular momentum and magnetic field at the horizon, and a smooth decay further away. We comment on the possibility of going beyond the leading order in perturbations and on its dynamical implications.

We study the Hawking temperature, geodesic motion, and observable signatures of the accelerating Bertotti-Robinson (BR) spacetime, a vacuum black-hole solution deformed by a uniform magnetic field $B$ and an acceleration parameter $\alpha$. In the timelike sector, we derive the effective potential for massive particles, determine the specific energy and angular momentum for equatorial circular orbits, and determine how $(B,\alpha)$ shifts the ISCO; we also illustrate representative trajectories of massive particles. We then compute the radial and latitudinal epicyclic frequencies for small perturbations about circular orbits, quantifying how the magnetic field and acceleration modify local radial and vertical stability. In the null sector, we derive the photon effective potential and obtain analytical expressions for the photon-sphere radius, critical impact parameter, and shadow radius, complemented by photon trajectories, the effective radial force, and the Lyapunov exponent controlling the instability of circular null orbits; we also provide parameter-space maps for the photon sphere and shadow. Finally, we obtain the energy emission rate emitted from the black hole, showing how the acceleration parameter and the magnetic field affect this.

The Hawking effect can be understood as a broad kinematic phenomenon associated with mode behavior near a horizon. While astrophysical black holes produce one specific realization of this radiation, this perspective inspires extensive theoretical and experimental efforts to create event horizons in diverse physical systems to observe the resulting analogue Hawking emission. One of the most successful realizations is the fiber-optical analogue, based on nonlinear quantum optics. In these notes, we introduce and motivate this system while outlining the theoretical concepts underlying the gravitational analogy. Finally, we review key experiments and discuss their impact on the field.

An explicit correspondence is established between the Extended Uncertainty Principle (EUP) and the metric function by directly relating the radiation temperature function modified by EUP to the modified spacetime metric. Utilising this modified metric, we subsequently derive the corresponding thermodynamic quantities of the black hole, and calculate the photon sphere radius and the size of the black hole shadow. The results of the study indicate that, in comparison with Schwarzschild black holes, the position of the event horizon remains constant under EUP modifications. However, the photon sphere radius increases with growing EUP parameters, while the shadow size decreases with increasing parameters, demonstrating that EUP induces optical shift phenomena. By comparing with observations of the galactic centre black hole $\text{Sgr}{\text{A}^{*}}$ from the Event Horizon Telescope, new constraints are established on EUP parameters.

Recently, an exact rotating black hole solution in a parity-violating theory of gravity was obtained via a conformal transformation of the Kerr solution in general relativity, with parity-violating effects encoded in the conformal factor. We study the quasinormal modes (QNMs) of a test scalar field minimally coupled to gravity on this conformal Kerr background, treating the parity-violating effects perturbatively while allowing for arbitrary black hole spin, from the non-rotating case to the near-extremal regime. For low spin, we derive a perturbative formula for the QNM frequencies that includes the leading-order parity-violating correction. For high spin, particularly in the near-extremal regime, we find sizable deviations from the Kerr QNM frequencies. Our results point to a new avenue for probing parity-violating physics in the strong-gravity regime through black hole QNMs.

In this work, we construct a locally inertial reference system adapted to a geodesic observer in stationary, axisymmetric dust solutions of the Einstein equations employed as effective models of a portion of a galactic disc. To ensure a consistent spatial orientation among different local observers, we also introduce the radially locked reference system, in which one spatial axis is aligned with the radial direction defined by null geodesics passing through the galactic center. Within this framework, we analyze how the dust configuration is described by such observers by computing the frequency shift of photons exchanged between pairs of dust geodesics. Building on this construction, we outline a procedure to reconstruct spectroscopic and astrometric relative velocities with respect to locally inertial observers, providing a coherent foundation for the study of galactic kinematics in a fully general relativistic context.

This study explores singularity-free solutions to the static, spherical symmetric Einstein equations with the standard Schwarzschild solution as a boundary condition. Imposing the absence of curvature singularities and requiring differentiability of the time component of the metric leads to a sign change across the horizon, violating the Principle of Equivalence locally. We find a solution within the event horizon with a simple ``cosmological constant'' stress-energy tensor. Considering the impact of sign change to a compact stellar remnant, modeled by an incompressible perfect fluid obeying the Tolman-Oppenheimer-Volkoff equation, we rediscover the same geometry, indicating both mathematical and physical feasibility of the model. We also find a new theoretical limit M/R=3/8, which is lower than the Buchdahl limit of M/R=4/9 for the density of a perfect fluid that will recede behind an event horizon. The equation of state is discussed, and we propose that the final state is described by a Higgs-like free scalar field.

A new phenomenological dark energy model, originally associated to the large-scale structure formation and considered as a solution to the fine-tuning and coincidence problems related to the cosmological constant, was analyzed within the framework of General Relativity in a Friedman-Robertson-Walker spacetime and its model parameters were estimated using cosmic chronometers and recent DESI data. It turns out that the proposed model can serve as an alternative evolving dark energy model with a novel equation of state function, apart from other popular propositions in the literature. Due to the form of this phenomenological energy density ansatz, which starts to rise with the nonlinear structure growth in the universe and falls with the domination of cosmic voids, we prefer to call it structure-induced dark energy. Observational constraints show that it is not only a suitable solution for the fundamental problems such as coincidence or fine-tuning problems, it gives flexibility, when considering the cosmic tensions and presents a new perspective on the evolving dark energy models.

We develop a systematic framework for formulating and solving the conditions that lead to separability in stationary, axisymmetric spacetimes in the presence of matter fields. Guided by Carter's metric form, we introduce a general stationary, axisymmetric metric ansatz that allows for a transparent separation of radial and angular variables. This construction yields a broad family of stationary rotating solutions admitting separability structures. To illustrate the applicability of the formalism, we explicitly construct several examples, including a rotating black hole with a global monopole supported by anisotropic matter, as well as a new class of rotating wormhole geometries.

We study slow-roll inflation driven by a scalar field non-minimally coupled to gravity within the effective framework of Loop Quantum Cosmology (LQC), including inverse-volume corrections. We consider two physically motivated classes of potentials, a Higgs-like quartic potential $V\propto\phi^{4}$ and string-inspired fractional monomial potentials $V\propto\phi^{p}$ with $p<1$. Working at first order in the slow-roll expansion, we derive analytic expressions for the inflationary observables, namely the scalar spectral index $n_s$, the tensor-to-scalar ratio $r$, and the running $\alpha_s\equiv dn_s/d\ln k$, and then solve the corrected background dynamics numerically to obtain quantitative predictions. Confronting these results with current observational constraints from Planck 2018 and ACT DR6, we find that the model can lie within the allowed region of the $(n_s,r,\alpha_s)$ parameter space, including a mild preference for slightly larger $n_s$, as suggested by recent ground-based measurements. We also compute the probability of achieving sufficient slow-roll inflation in this setting. Although effective LQC replaces the initial singularity with a nonsingular quantum bounce, the likelihood of a sufficiently long inflationary phase depends on the pre-inflationary dynamics and on the inflaton potential. Using the canonical Liouville measure on the effective phase space, we determine the fraction of post-bounce trajectories that yield sufficient inflation and find that the non-minimal coupling parameter $\xi$ substantially enlarges the phase-space volume of favorable initial conditions relative to the minimally coupled case, exhibiting an attractor-like enhancement that saturates at large $\xi$.

We construct nonlinear wave operators and prove small-data asymptotic completeness for the Maxwell--Higgs system on the domain of outer communications of every four-dimensional subextremal Kerr black hole $(\mathcal D_{M,a},g_{M,a})$ with $M>0$ and $|a|<M$, for gauge-invariant nonnegative scalar potentials $P$ satisfying Assumption~\ref{asumsiP} with mass parameter $m^{2}\ge0$. The massless case $m=0$ is unconditional on the full subextremal range. For $m^{2}>0$ the same conclusions follow assuming the massive linear package $\Lin_{k}^{(m)}$ for the linear comparison system (in particular, no exponentially growing modes); this fails for an open set of masses due to superradiant instability \cite{ShlapentokhRothmanKGKerr}. We work in the radiative (charge-free) regime; stationary Coulomb (Kerr--Newman) modes are treated separately. Asymptotic states are described by gauge-covariant radiation fields on $\mathcal I^{\pm}\cup\mathcal H^{\pm}$ (and, when $m>0$, an additional timelike/Dollard channel), yielding a gauge-invariant nonlinear scattering map on the residual-gauge quotient. The scattering map is a small-data bijection, is Fréchet differentiable at $0$ with derivative equal to linear Kerr scattering, admits a quadratic (Born) expansion with an $O(\|U\|^{3})$ remainder in the natural asymptotic topology, and is real-analytic for analytic $P$. The nonlinear argument is presented as a transfer principle from a black-box linear estimate package for inhomogeneous Klein--Gordon and charge-free Maxwell fields, verified here in the massless Kerr case (and proved self-contained in Schwarzschild).

Hermiticity is usually treated as a foundational axiom of quantum mechanics, guaranteeing real spectra and unitary time evolution. In this work we argue that Hermiticity is more naturally understood as a symmetry law arising from the global conservation of an inner product current. We show that in spacetimes admitting complete Cauchy surfaces without boundary flux this conservation reduces to the familiar Hermiticity condition of the canonical inner product. However, in the presence of causal horizons, most strikingly in black hole geometries, this conservation law becomes obstructed for restricted observers. Tracing over inaccessible degrees of freedom then inevitably yields completely positive trace preserving dynamics with an effective non-Hermitian generator. Using quantum thermodynamics and the monotonicity of relative entropy, we demonstrate that the generalized second law may be reinterpreted as an entropy balance that compensates precisely for the flux of inner product charge through the horizon. The structure of Einstein equations, through the Bianchi identity and the Raychaudhuri focusing equation, provides the geometric mechanism underlying this balance. We also show that black hole ringdown can serve as a realistic observational probe of this idea and may provide quantitative upper bounds on the strength of horizon-induced inner product flux. In this way gravity, entropy production, and effective non-Hermiticity are unified under a single structural principle, with Hermiticity emerging as the special case of globally conserved inner product symmetry.

We investigate the effects, stability, and nonlinear dynamics of ghost scalar matter modeled as a field with a negative kinetic term confined within the cores of neutron stars. To this end, we analyze static configurations of the coupled Einstein-Euler-(ghost, complex) Klein-Gordon system and then we perform fully dynamical numerical evolutions of illustrative cases. Our results demonstrate that neutron stars can gravitationally confine a finite amount of ghost matter and support continuous families of equilibrium solutions, indicating that these configurations are not the result of fine tuning. We analyze the properties of the final states and find that the neutron star undergoes a persistent pulse-like oscillatory motion. In particular, we explicitly compute the frequency synchronization between the stellar fluid oscillation modes and those of the ghost scalar sector.

Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, where the number of accessible configurations $W(N)$ grows exponentially with the number of degrees of freedom~$N$. However, this framework breaks down for systems with strong correlations or long-range interactions, for which the configuration space exhibits non-exponential growth. While numerous generalized entropies have been proposed to address this limitation, a coherent link to classical thermodynamic laws has remained elusive. Here, we propose group entropies as a unifying framework, defining universality classes of entropies through the asymptotic scaling of $W(N)$, each yielding an extensive entropy. We show that this approach provides the basis for a consistent thermodynamic formulation beyond the Boltzmann--Gibbs paradigm. In particular, by expressing these entropies in terms of thermodynamic state variables and taking the thermodynamic limit, we demonstrate their consistency with classical thermodynamics, in close analogy to the emergence of the Clausius entropy from the Boltzmann--Gibbs formalism. Focusing on the zeroth thermodynamic law, we identify the empirical temperature and, by using Carathéodory's formulation of the second law, we derive the associated absolute temperature. As an application of the thermodynamic framework obtained, we analyze black-hole thermodynamics using the group entropy class corresponding to stretched-exponential behavior of $W(N)$. In particular, we show that a hallmark property of black holes -- their negative specific heat -- emerges naturally within this framework while the entropy remains extensive. This result holds for the stretched-exponential entropies associated with both the Bekenstein--Hawking and Barrow entropy scalings.

We investigate an approach to determine the correct Poisson brackets of fields restricted to codimension 2 and 3 surfaces in 4D gravity, which are of great potential use in holographic setups and discretisation. Employing a specific BF-BB type parametrisation of gravity which relaxes Plebanski's simplicity constraints, we find that gravity in 4 dimensions carries Chern-Simons like phase spaces in codimension 2 and Kac-Moody algebras in codimension 3. The necessary gauge algebra in this context shows that the appropriate generalisation of the double $\mathcal{D}\mathfrak{so}(1,2)$ of 3D gravity is the Maxwell algebra, $\mathfrak{g}=\mathfrak{so}(1,3)\ltimes(\mathbb{R}^{1,3}\tilde\oplus \mathfrak{so}(1,3)^\ast)$. This realises the corner Poisson bracket of the spin connection for the first time and shows it is off-shell commutative, while the corner metric is noncommutative.

Stage-IV photometric galaxy surveys are designed to measure the position and shapes of billions of galaxies. Their aim is to characterise the large-scale distribution of matter in the Universe using galaxy clustering and weak gravitational lensing. As a byproduct, stage-IV surveys are expected to detect more than a hundred thousand strong gravitational lenses. In this article, we propose the use of weak-lensing perturbations to strong lenses, specifically their line-of-sight (LOS) shear, as a cosmological probe. This new observable allows us to define three new correlation functions: the LOS shear with itself, with galaxy positions, and with galaxy shapes, thereby promoting the standard $3\times 2$pt correlation method to a $6\times 2$pt scheme. We design estimators for these new correlation functions and determine their expectation values as a function of the matter power spectrum. We then derive the analytical expression for the full covariance matrix of the $6\times 2$pt correlation scheme. Considering various scenarios for the stage-IV strong-lensing samples, we demonstrate that the cosmological information carried by the LOS shear of strong lenses will be detectable with a very high signal-to-noise ratio, even in the most pessimistic of cases. Strong lenses are thus extremely promising cosmological probes, whose synergy with galaxy positions and shapes should also contribute to mitigating systematics in stage-IV surveys.

The precision era of multi-messenger astronomy, together with modern astrophysical, cosmological, and gravitational wave observations, increasingly points toward the existence of a ``dark" sector that cannot be explained within the framework of the Standard Model of particle physics and General Relativity. In this review, we explore extensions of standard physics and examine how observational data can be used to probe new particles and interactions. We consider a wide range of scales, from Solar System tests to galactic and cosmological observations, and investigate both conventional dark matter candidates, such as weakly interacting massive particles, and alternative scenarios including ultralight fields and primordial black holes. We discuss constraints derived from compact objects such as neutron stars, black holes, pulsars, and magnetars observations as well as from high-energy astrophysical phenomena. In addition, we analyze extensions of General Relativity involving additional scalar fields and their impact on gravitational wave signals and stochastic backgrounds from primordial black holes. We also study the capture and accumulation of dark matter in compact objects, which can alter properties such as mass, radius, and tidal deformability, and consider scenarios in which dark matter decays into Standard Model particles. While current observations already place significant limits on dark matter and modified-gravity models, upcoming experiments and observatories are expected to further probe or discover such new physics by improving constraints on particle masses and interaction strengths.

A recently proposed generalized entropy by Luciano and Saridakis extends the standard Boltzmann-Gibbs and Bekenstein-Hawking framework through a microscopically motivated construction involving two independent entropic exponents. When applied within the gravity-thermodynamics correspondence, this entropy leads to a modified cosmological dynamics that can be interpreted as an effective dark energy sector of entropic origin, while recovering $\Lambda$CDM in appropriate limits. In this work, we perform the first observational confrontation of the resulting entropic cosmology at the background level. Focusing on the case $\alpha_\delta=0$, we constrain the model using Cosmic Chronometers, Pantheon$^+$ Type Ia supernovae calibrated with SH0ES, BAO measurements from DESI DR2 and compressed Planck 2018 CMB information. We find that the model yields a statistically robust fit to the combined data sets and can simultaneously satisfy Pantheon$^+$, SH0ES and CMB shift-parameter constraints, unlike $\Lambda$CDM. Although the entropic parameters remain close to their standard values, the $\Lambda$CDM limit is excluded at the $2\sigma$ level within the restricted parameter space considered. These results indicate that the Luciano-Saridakis entropic cosmology offers a viable extension of the standard model with the potential to alleviate the Hubble tension at the background level.

We investigate the principles of quantum field theory using a stiff de Sitter space. We demonstrate that a non-unitary Lagrangian on a Euclidean AdS geometry can produce the perturbative expansion of late-time correlation functions to all orders. This discovery greatly simplifies perturbative computations while also allowing us to prove fundamental features of these correlators, which are part of a Euclidean CFT. This allows us to construct an OPE expansion, limit the operator spectrum, and deduce the analytic structure of the spectral density that captures the conformal partial wave expansion of a late-time four-point function. In general, the standard CFT concept of unitarity does not apply to dimensions and OPE coefficients. Rather, the positivity of the spectral density represents the unitarity of the de Sitter theory. This assertion is non-perturbative and does not depend on the use of Euclidean AdS Lagrangians. In a scalar theory, we compute tree-level and entire one-loop-resummed exchange diagrams to demonstrate and verify these characteristics. In the spectrum density, an exchanged particle shows up as a resonant characteristic that may be helpful in experimental searches.

It is mandatory to know how to operationally define and translate a reference frame into mathematics, in order that a physical interpretation of theory calculations in terms of observational data is possible. The situation is particularly challenging for gauge systems such as General Relativity where spacetime coordinates are subject to spacetime diffeomorphisms considered as gauge transformations turning coordinates into non-observables. This motivates the idea of operationally defined (material) reference frames which specify coordinates in terms of matter or geometry reference fields leading to the concept of relational observables, relational reference frames and gauge reduction. Upon quantisation, all fields become operator valued distributions. Now new conceptual and technical questions arise such as: Should one reduce before or after quantisation and how are the reference fields quantised respectively in either route? Is a reference frame itself subject to quantisation and how are different quantum reference frames related? How does the gauge reduction fit into this, i.e. how can it be that a certain reference field is considered a non-observable in one reference frame and an observable in another which upon quantisation even displays fluctuations? How precisely are gauge dependent fields interpreted in terms of the relational observables in a given reference frame? What is the relative dynamics, e.g. how exactly are physical Hamiltonians of two relational reference frames related? The present conceptual work addresses these and related questions in a non-perturbative field theory context of sufficient generality to cover General Relativity coupled to standard matter. A central role is played by the concept of the relational reference frame transformation (RRFT) for which a general formula is derived and its properties are explored.

Can we infer whether all of physical reality began to exist? Several novel results are offered suggesting a negative verdict. First, a common strategy for defending a cosmic beginning involves showing that individual beginningless cosmological models are implausible. This strategy is shown to make an elementary error in confirmation theory. Second, two necessary (but not necessarily sufficient) conditions are offered for a cosmic beginning. Third, three extensions are offered to the Malament-Manchak theorems. The three extensions show that in almost all classical spacetimes, observers cannot collect sufficient data to determine whether the application conditions for the classic singularity theorems are satisfied or whether their spacetime satisfies the two necessary conditions for a cosmic beginning. Lastly, a reply is offered to the objection that the skeptical consequences of the three extensions can be overcome with induction. Importantly, all past singular dust FLRW spacetimes have observationally indistinguishable counterparts which, while sharing a number of important local properties, either do not include a singularity to the past of every point or else do not have the sort of time ordering intuitively required for a cosmic beginning.

In the excursion-set formalism, the mass distribution of primordial black holes (PBHs) is derived from the first-passage time of a random walk describing the density contrast as the coarse-graining scale varies. We address two recent criticisms that have been raised about this approach. First, it was argued that the random walks are subject to colored (i.e. correlated over time) noise, making the first-passage-time problem cumbersome. We show that this arises from an incorrect separation of drift and noise when sampling on the Hubble-crossing surface: if Fourier modes are uncorrelated, the noise is strictly white. Moreover, sampling along the Hubble-crossing surface precludes using the density dispersion as a time variable, explaining the reported pathologies. Sampling instead on a synchronous surface removes both issues. This requires solving a first-passage-time problem with a moving barrier, for which we provide an efficient numerical framework. Second, it was suggested that cloud-in-cloud (i.e. that large black holes may engulf smaller ones) is irrelevant for PBHs and that the excursion set is therefore not needed. While valid for widely separated scales, this statement fails for broad power spectra with enhanced continua of modes. We further show that Press-Schechter estimates neglecting boundary evolution can break down even without cloud-in-cloud effects. Our results establish the robustness and necessity of the excursion-set formalism in realistic PBH formation scenarios.

We investigate the relativistic scattering of spinning black holes using modern amplitude methods within a heavy-mass effective field theory formalism at third post-Minkowskian order. Using a systematic self-force expansion up to first order in the mass ratio, the gravitational amplitude and the associated eikonal-like phase are computed for a spin-aligned binary system comprising a heavy and a light black hole up to fifth order in the total spin and up to quadratic order in the spin of the light black hole. We also consider the resummation of the heavy black hole's spin in both the probe limit and the radiation-reaction sector, and verify that the resulting phase displays the characteristic ring singularity features associated with the Kerr metric.

Wave-optics effects in strongly lensed gravitational waves (GWs) provide a new interferometric probe of dark matter substructure. We compute the full diffraction integral for GWs propagating through statistically generated cold dark matter subhalo populations and quantify the resulting frequency-dependent amplification in the Laser Interferometer Space Antenna (LISA) band. We show that realistic galaxy-scale lenses generically produce percent-level amplitude and phase distortions in strongly magnified images, primarily induced by subhalos in the mass range $10^4$-$10^7\,M_{\odot}$. These signatures arise naturally within the standard cold dark matter paradigm and should be detectable in high signal-to-noise LISA events. Strongly lensed GWs thus offer a direct and complementary window on dark matter structure at subgalactic mass scales inaccessible to electromagnetic measurements.

Single-minus tree-level $n$-graviton scattering amplitudes are revisited. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. A Berends-Giele recursion relation for these amplitudes is derived and solved in a form involving a sum over trees. In a restricted kinematic decay region, this solution simplifies significantly to an $(n{-}2)$-fold product of soft factors. It is further shown in this region that, combined with suitable analyticity assumptions, the $n$-graviton amplitude is generated by a recursive $\mathcal{L}w_{1+\infty}$ Ward identity with the three-graviton amplitude as a seed.

The field of gravitational waves is rapidly progressing due to the noticeable advancements in the sensitivity of gravitational-wave detectors that has enabled the detection prospects of binary black hole mergers. Extreme mass ratio inspiral (EMRI) is one of the most compelling and captivating binary systems in this direction, with the detection possibility by the future space-based gravitational wave detector. In this article, we consider an EMRI system where the primary or the central object is a spherically symmetric static braneworld black hole that carries a \textit{tidal charge} $Q$. We estimate the effect of the tidal charge on total gravitational wave flux and orbital phase due to a non-spinning secondary inspiralling the primary. We further highlight the observational implications of the tidal charge in EMRI waveforms. We show that LISA (Laser Interferometer Space Antenna) observations can put a much stronger constraint on this parameter than black hole shadow and ground-based gravitational wave observations, which can potentially probe the existence of extra dimensions.

The longstanding issue of general covariance in effective models of quantum gravity is addressed, which arises when canonical quantum gravity leads to a semiclassical model described by an effective Hamiltonian constraint. In the context of spherically symmetric models, general covariance is precisely formulated into a set of equations, leading to the necessary and sufficient conditions for ensuring covariance. With the aid of these conditions, we derive the equations for the effective Hamiltonian constraint. The equations yield two candidates for effective Hamiltonian constraints dependent on a quantum parameter. The resulting quantum modified black hole spacetimes are analyzed. Our models show improvement by casting off the known limitations of previous works with similar results.

The issue of general covariance in effective quantum gravity models within the Hamiltonian framework is addressed. The previously proposed equations for the covariance condition in spherically symmetric models are explicitly derived. By solving this equation, a new effective Hamiltonian constraint is obtained, incorporating free functions that can account for quantum gravity effects. The resulting spacetime structure is analyzed by specifying the free functions. Remarkably, in this model, the classical singularity is replaced by a region where the metric asymptotically approaches a Schwarzschild-de Sitter one with negative mass. Thus, this new quantum-corrected black hole model avoids the Cauchy horizons presented typically in previously studied models. The covariant approach is also applicable to matter coupling in the models.

Extreme mass-ratio inspirals (EMRIs), in which a solar mass compact object is whirling around a supermassive black hole, act as precise tracers of the spacetime geometry and astrophysical environment around the supermassive black hole. These systems are highly sensitive to even the smallest deviations from the vacuum general relativity scenario. However, detecting these signals requires highly accurate waveform modeling up to the first post-adiabatic order, incorporating self-force effects, system parameters, and environmental influences. In this paper, we focus on the impact of dark matter on gravitational waveforms. Cold dark matter in galactic centers can be redistributed by the gravitational pull of a supermassive black hole, forming a dense, spike-like profile. When an EMRI evolves in such an environment, the interaction between the binary and the surrounding dark matter can leave distinctive imprints on the emitted waveform, and thus offer a novel way to probe the nature and distribution of dark matter. We specifically examine how dark matter modifies the background spacetime. By treating these modifications perturbatively, we present a framework to incorporate dark matter environmental effects into gravitational waveform modeling at the first post-adiabatic order.

Recent years have seen the first production of "post-adiabatic" gravitational-waveform models based on second-order gravitational self-force theory. These models rely on calculations of an effective source in the perturbative second-order Einstein equation. Here, for the first time, we detail the calculation of the effective source in a Schwarzschild background, which underlies the second-order self-force results in [Phys. Rev. Lett. 127, 151102 (2021); ibid. 128, 231101 (2022); ibid. 130, 241402 (2023)]. The source is designed for use in the multiscale form of the Lorenz-gauge Einstein equation, decomposed in tensor spherical harmonics, or in the analogous second-order Teukolsky equation. It involves, among other things, contributions from (i) quadratic coupling of first-order field modes, (ii) the slow evolution of first-order fields, (iii) quadratic products of a first-order puncture field, and (iv) the second-order puncture field. We validate each of these pieces through numerical and analytical tests.

In the framework of quasi-topological (QT) gravity, we propose a novel model which is characterized by a bounce of the spacetime such that the singularity in standard general relativity can be avoided in both cosmological and black hole setups. Specifically, in the cosmological background, this model reproduces the modified Friedmann equation proposed in loop quantum cosmology, while in a black hole background, it produces a black bounce metric identical to that of the quantum Oppenheimer-Snyder (qOS) model. This model resolves the singularity presented in the qOS model as well as in QT gravity coupled to linear electromagnetic fields, and provides a unified, manifestly covariant framework for general spacetimes, from which both the modified Friedmann equation and the qOS black hole metric can be derived. Furthermore, it establishes a profound correspondence between the effective dynamics of loop quantum cosmology and the QT gravity theory, suggesting that certain quantum gravitational effects in loop quantum gravity can be captured by adding an infinite tower of higher-curvature corrections to the Einstein-Hilbert action.

In the single-field case, Horndeski provides the most general scalar-tensor theory with second-order field equations. By contrast, systematic multi-field extensions remain incomplete: while the general field equations for the bi-Horndeski case are known, a general action has not been established, and for cases with three or more fields, neither a general action nor general equations are available. We characterize Horndeski by two mild axioms: closure under invertible pure disformal transformations and the requirement that the theory includes the minimal Horndeski theory. Under this characterization, we recover the standard single-field action up to boundary terms and obtain a practical path to multi-field constructions. In particular, we show that antisymmetric structures, such as those identified by Allys, Akama, and Kobayashi, appear within this framework, and indicate that this viewpoint has the potential to account for features captured by known bi-Horndeski equations.

We study null geodesics that connect the two asymptotically flat regions of the maximally extended Kerr spacetime. These vortical geodesics traverse both horizons and pass through the ring singularity, linking the positive-$r$ exterior to the negative-$r$ asymptotic side. Using impact parameters, we identify a closed subset of parameter space, the inner throat, where the radial potential has no real roots, and photons exhibit no radial turning points. In this region, at most two constant-latitude geodesics exist, one of which is aligned with the principal null direction. We also identify the forbidden polar-angle band that limits the range of geodesics reaching an asymptotic observer. We solve the geodesic equations analytically and numerically in Eddington-Finkelstein-like coordinates, obtaining mutually consistent results that correct and extend previously available formulae. The resulting trajectories are used to construct simulated views for an observer in the negative-$r$ domain, revealing strong image distortion and inversion, with possible implications for analogous white-hole configurations.

There exist several different proposals for a measure in Quantum Gravity theories. Although sometimes being labelled as non covariant, the measure derived in [7] for GR has the particularity that, in the extremal, the volume divergences cancel out. The analogous for Quadratic Gravity [1]-[2] was considered in [44]-[45]. However, as far as the author knows, the issue of volume divergences was not considered for this last measure. The present work fills this gap and presents an analysis showing that, in the extremal, these divergences cancel as well. This is up to some subtleties related to superdeterminants. The possibility of employing non invariant measures may be accepted if the anomaly in the measure is compensated by counter term redefinitions of the model under analysis. This makes difficult to disprove, at the present times, some choices of measures. Quadratic Gravity[1]-[2], is known to be renormalizable in flat space, and there are a finite number of counter terms needed in order to renormalize its effective action. However, around a curved space this is not known, and this complicates considerably the analysis. These issues are reviewed in the text, together with an analysis of covariant measures. In particular, it is shown how these measures [47]-[49] can be found if one condition in [7] is relaxed.

Regular black holes are often used to address singularities, but they typically involve a potentially unstable de Sitter core and an internal horizon that breaks predictability. Integrable singularities (IS) have recently gained attention because they avoid both issues and exhibit finite tidal forces, allowing nondestructive radial infall. First, we present a new BH solution sourced by a string fluid (FS) that exhibits an IS. Motivated by the divergence of the conserved energy in the cloud of strings (CS) model, we introduce an energy density profile based on the screening of the CS energy density within an FS framework, thereby yielding finite conserved energy. On the other hand, the idea that an interior region, rather than a pointlike mass, can generate a Schwarzschild black hole exterior region has recently gained attention \cite{Ovalle:2024wtv,Maeda:2024tpl}. This is obtained by matching an interior solution to the Schwarzschild exterior at the event horizon. Secondly, motivated by the variety of singular BH solutions in the literature, we establish the conditions that an interior region with an IS must satisfy in order to represent the interior of a generic exterior BH solution, with Schwarzschild being only a particular case of the latter. We derive the junction conditions (JC) between the interior and exterior regions, showing that they lead to temperature continuity at the interface, while discontinuities in tangential pressure lead to phase transitions. We propose that the nature of the interior region is described by CS and FS, while the exterior corresponds to Reissner Nordström.

We investigate the shadow cast by a rotating traversable wormhole in the Teo class endowed with a general redshift function, with particular emphasis on the emergence of cuspy structures. The shadow boundary is the common envelope of two critical orbit families: unstable circular orbits outside the throat and orbits at the throat itself. The formation of cusps, marking the transition between smooth and cuspy shadow boundaries, only becomes possible when the redshift parameter $\lambda$ is allowed to vary. Moreover, we uncover a universal critical value $\lambda_c$ that signals the onset of the cusp. A phase diagram characterized by the spin and redshift parameters reveals four distinct morphologies: smooth, cuspy, ears touching, and throat drowning. The morphology of the wormhole shadow may provide observational diagnostics for the different compact objects in future high-resolution imaging observations.

We extend the first order dissipative relativistic hydrodynamics model of Bemfica-Disconzi-Noronha- Kovtun (BDNK) in order to include the charge number current in full first order expansion with out-of-equilibrium contribution proportional to the evolution equation of the ideal fluid. We obtain a fully second order system of partial differential equation (PDE) that can be casted in a fully conservative way. We analyze the hyperbolicity of this model coupled to Einstein field equations using a newly developed technique that allows for hyperbolicity studies without explicit first order reduction. Furthermore, we identify a frame choice where our formulation is causal, stable and with positive entropy generation for a wide range of equations of state (EoS). Our analysis shows that the inclusion of an out-of-equilibrium correction to the charge current, plays an important role in guaranteeing the strong hyperbolicity and, therefore, the well-posedness of the system. If such correction is not applied, an extra frame restriction must be added to the present in the literature in order to obtain a strongly hyperbolic system.

We study relative differential and integral forms on families of supermanifolds and their cohomology. We prove a relative Poincaré--Verdier duality and show that it relates the cohomology of differential and integral forms, admitting a concrete geometric realization via Berezin fiber integration. We further introduce the Poincaré--dual integral form associated to an embedded even family and prove that it satisfies the correct localization property. We then apply these results to supergravity, focusing on the $3d$ case. In this setting, we show that relative Poincaré duality provides the natural framework for encoding the data needed to relate a superspace formulation to the physical spacetime, thereby yielding a rigorous definition of picture changing operators used in the physics literature. Building on this, after a careful analysis of the space of fields and the relevant constraints, we prove that the component, superspace, and geometric formulation of the theory are all equivalent. Finally, under suitable hypotheses, we argue that our construction illustrates a general principle governing the mathematical formulation of classical field theories on supermanifolds.

We analyze the domain of validity of a quantum optical model that describes the effects of gravitational redshift on the quantum state of photons that propagate in curved spacetime. This model assumes that the modes defining the initial state of the photon are mixed with an auxiliary environment mode via an effective multimode mixer. We find that the model, as proposed, is consistent only to first order for small redshift, where the range of validity is conditional not only to the gravitational parameters, but also to those that define the photonic modes. We identify the problem and provide a partial solution in terms of a necessary condition on the transformation matrix representing the process, which requires the use of a number of auxiliary modes that is at least equal to the number of modes that define the photonic state. We conclude by discussing implications for theoretical quantum optics and photonics in curved spacetime, as well as for the development of quantum technologies.

In this paper, we develop a method to extract the Bekenstein-Hawking entropy of $D$-dimensional black holes using the entanglement entropy of a lower-dimensional conformal field theory (CFT). This approach relies on two key observations. On the gravitational side, the near-horizon geometry of extremal black holes is AdS$_{2}$, and the Bekenstein-Hawking entropy is entirely determined by this two-dimensional geometry. Moreover, the higher-dimensional spherical part of the black hole metric is absorbed into the $D$-dimensional Newton's constant $G_{N}^{\left(D\right)}$, which can be effectively reduced to a two-dimensional Newton's constant $G_{N}^{\left(2\right)}$. On the field theory side, the entanglement entropy of two disconnected one-dimensional conformal quantum mechanics (CQM$_{1}$) can be calculated. According to the Ryu-Takayanagi (RT) prescription, this entanglement entropy computes the area of the minimal surface in the AdS$_{2}$ geometry. Since the near-horizon region of the black hole and the emergent spacetime derived from the entanglement entropy share the same Penrose diagram -- with both the black hole event horizon and the RT surface corresponding to specific points on this diagram -- the Bekenstein-Hawking entropy can be probed via entanglement entropy when these points coincide. This result explicitly demonstrates that the entanglement across the event horizon is the fundamental origin of the Bekenstein-Hawking entropy.

In the thin wall approximation, we study a class of asymptotically AdS black holes which contain a spherically symmetric vacuum bubble with a different (positive or negative) cosmological constant. Collapsing, expanding, and static bubble solutions are considered. Among these, expanding bubbles with positive cosmological constant can provide a way to apply the AdS/CFT correspondence to describe the physics of an expanding universe. We systematically study the causal structure of the solutions as a function of the cosmological constant, the mass of the black hole, and the tension of the bubble. We then compute the holographic entanglement entropy for a class of boundary subregions using extremal codimension-two surfaces as a probe. For collapsing bubbles, we find examples in which the entanglement entropy also explores the geometry inside the black hole bifurcation surface. As a complementary way to probe the interior of the bubble, we investigate almost-null radial geodesics related to the bulk-cone singularities of boundary two-point correlators. While the bulk-cone singularities for collapsing and expanding bubbles are consistent with thermalization at late time, static bubbles violate thermalization and exhibit properties similar to those of scar states.

Carrollian manifolds offer an intrinsic geometric framework for the physics in the ultra-relativistic limit. The recently introduced Carrollian Lie algebroids are generalised to the setting of $\rho$-commutative geometry, (also known as almost commutative geometry), where the underlying algebras commute up to a numerical factor. Via $\rho$-Lie-Rinehart pairs, it is shown that the foundational tenets of Carrollian geometry have analogous statements in the almost commutative world. We explicitly build two toy examples: we equip the extended quantum plane and the noncommutative $2$-torus with Carrollian structures. This opens up the rigorous study of noncommutative Carrollian geometry via almost commutative geometry.

We revisit the computation of the shear viscosity to entropy ratio $\eta/s$ at finite chemical potential in a holographic model that takes into account the quantum fluctuations in the IR region of near-extremal black branes. Such quantum corrections can be computed from JT gravity and generate non-trivial temperature dependence for $\eta/s$, which deviates from the universal $1/4\pi$ result. In the semi-classical regime, $\eta/s$ attains a minimum which is below the KSS bound, generated by the presence of the quantum effects. In the quantum regime at lower temperatures, $\eta/s$ increases and is well above the KSS bound. We also compare the shear viscosity to the quantum-corrected absorption cross-section of near-extremal black holes, and find agreement.

Whereas local field operators play the crucial role in reconciling quantum mechanics and special relativity, they are not trivially compatible with the diffeomorphism invariance of gravity. In order to address this issue, we consider the background geometry which breaks the isometry spontaneously. Then the local gauge invariant operator can be constructed through the Stückelberg mechanism, where the fluctuation of the metric in the direction of the isometry breaking combines with that of matter whose classical solution breaks the isometry. This is equivalent to introducing the clock and the rod to promote the local field operators to the gauge invariant ones. A typical example is the curvature perturbation in quasi-de Sitter space arising from the spontaneous breaking of the timelike isometry. We also discuss the features of the local gauge invariant operator when the spacelike isometry is spontaneously broken. Meanwhile, even if the local gauge invariant operators exist, it does not guarantee the reliable construction of the gauge invariant operators on the local region like the island, which is regarded as an essential ingredient to resolve the black hole information paradox. This is because the fluctuation of the spacetime point is accumulated in time, which in fact also gives rise to eternal inflation in quasi-de Sitter space. In order to suppress the fluctuation at late time, the isometry must be strongly broken by the background. In the case of the evaporating black hole, it may be achieved by the transition to the higher dimensional black hole.

We investigate whether Newtonian gravity can generate quantum entanglement between mesoscopic quantum bodies modeled as superposed mass quadrupoles using three complementary approaches: mini-superspace, semiclassical gravity, and stochastic gravity. We systematically analyze gravitationally induced entanglement (GIE) mechanisms and the conditions under which they can arise. Our results support the GIE hypothesis by showing that the mini-superspace framework, which quantizes the parity of the gravitational tidal field, can entangle spatially separate quantum bodies. In contrast, the semiclassical and stochastic gravity models, in which the tidal gravitational field sourced by the quantum bodies remains classical, fail to entangle the final state. These findings clarify recent claims that classical gravity might induce entanglement, and reveal how perturbative treatments can lead to misleading conclusions.

The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility for an observer to access its own quantum state of motion. This results in a fully relative formulation of quantum mechanics with observer-dependent Hilbert spaces, relative quantization rules, and novel uncertainty relations, while also elucidating some interpretational issues present in the current formulation of quantum mechanics and giving experimentally testable signatures.