Black holes are assumed to decay via Hawking radiation. Recently we found evidence that spacetime curvature alone without the need for an event horizon leads to black hole evaporation. Here we investigate the evaporation rate and decay time of a non-rotating star of constant density due to spacetime curvature-induced pair production and apply this to compact stellar remnants such as neutron stars and white dwarfs. We calculate the creation of virtual pairs of massless scalar particles in spherically symmetric asymptotically flat curved spacetimes. This calculation is based on covariant perturbation theory with the quantum field representing, e.g.,\ gravitons or photons. We find that in this picture the evaporation timescale, $\tau$, of massive objects scales with the average mass density, $\rho$, as $\tau\propto\rho^{-3/2}$. The maximum age of neutron stars, $\tau\sim 10^{68}\,\text{yr}$, is comparable to that of low-mass stellar black holes. White dwarfs, supermassive black holes, and dark matter supercluster halos evaporate on longer, but also finite timescales. Neutron stars and white dwarfs decay similarly to black holes, ending in an explosive event when they become unstable. This sets a general upper limit for the lifetime of matter in the universe, which is much longer than the Hubble--Lema\^itre time. Primordial objects with densities above $\rho_\text{max} \approx 3\times 10^{53}\,\text{g/}\text{cm}^3$, however, should have dissolved by now. As a consequence, fossil remnants from a previous universe could be present in our current universe only if the recurrence time of star forming universes is smaller than about $\sim 10^{68}\,\text{years}$.

Massive scalar fields are promising candidates to address many unresolved problems in fundamental physics. We report the first model-agnostic Bayesian search of massive scalar fields in LIGO/Virgo/KAGRA gravitational-wave data. We find no evidence for such fields and place the most stringent upper limits on their coupling for scalar masses $\lesssim 2\times10^{-12}\,{\rm eV}$. We exemplify the strength of these bounds by applying them to massive scalar-Gauss-Bonnet gravity, finding the tightest constraints on the coupling constant to date, $\sqrt{\alpha_{\rm GB}}\lesssim 1\,{\rm km}$ for scalar masses $\lesssim 10^{-13}\,{\rm eV}$ to 90% confidence.

In this paper we examine the relativistic Einstein rings assuming a nonminimal coupling between gravitation and electromagnetism in a Reissner-Norstr\"om background. Starting from a general action of a nonminimal coupled electrodynamics we show that an unstable effective photon sphere may be obtained in the regime of eikonal approximation. Apart from it, an inner stable photon sphere may also be obtained in the case of large coupling parameters and/or nearly extremal configurations. Restricting ourselves to the outer unstable photon sphere domain we examine the expected angular positions of the first and second relativistic Einstein rings. To compare our results with previous studies in the literature we model the lens as a Galactic supermassive black hole. For fixed coupling parameters we show that such angular positions decrease as the charge parameter increases. The angular separation between the first and second rings is also evaluated. We show that such separation increases as the charge parameter increases. These patterns are not followed by nearly extremal configurations. In this case we show that there is an overlap domain so that the angular position and the corresponding coupling parameter do not allow one to differ extremal cases from complementary configurations which satisfy the cosmic censorship hypothesis.

We investigate the degrees of freedom of new general relativity. This theory is a three-parameter theory and is classified into nine irreducible types according to the rotation symmetry of $SO(3)$ on each leaf of ADM-foliation. In this work, we focus on unveiling the degrees of freedom of the physically interesting types of NGR: Type 2, Type 3, Type 5, and Type 8, which contain the gravitational propagating degrees of freedom. First, we revisit the theory based on the gauge approach to gravity and reformulate the Lagrangian of the theory. Second, we review the irreducible decomposition of the theory while focusing on the Hamiltonian and the primary constraints in each type. Third, we perform the Dirac-Bergmann analysis to unveil the degrees of freedom of the theory in the case of Type 2, Type 3, Type 5, and Type 8. We find a novel new behavior of constraints in Type 8, which is classified as second-class but not to determine any Lagrange multipliers and to provide the gauge invariance of the theory under the satisfaction of a specific condition of the multipliers. The degrees of freedom of Type 2, Type 3, and Type 5 are unveiled as six, five, and seven, respectively. The degrees of freedom of Type 8 is either four under a specific condition to the Lagrange multipliers or six in the generic case. Finally, we conclude this work with several future perspectives.

In this paper, we investigate the properties of black holes within the framework of multi-fractional theories of gravity, focusing on the effects of q-derivatives and weighted derivatives. These modifications, which introduce scale-dependent spacetime geometries, alter black hole solutions in intriguing ways. Within these frameworks, we analyze two key observable phenomena - black hole shadows and particle deflection angle in the weak field limit - using both analytical techniques and observational data from the Event Horizon Telescope (EHT) for M87* and Sgr A*. The study from $q$-derivative formalism reveals that the multi-scale length $\ell_*$ influences the size of the black hole shadow in two ways, and modifies the weak deflection angle. Constraints on $\ell_*$ are derived from the EHT observations, showing significant deviations from standard Schwarzschild black hole predictions, which range from $10^{9}$ to $10^{10}$ orders of magnitude. Additionally, the weak deflection angle is computed using the non-asymptotic generalization of the Gauss-Bonnet theorem, revealing the effects of finite-distance and multi-scale parameters. Using the Sun for Solar System test, the constraints for $\ell_*$ range from $10^{8}$ to $10^{9}$ orders of magnitude. Results from the weighted derivative formalism generates a dS/AdS-like behavior, where smaller deviations are found in the strong field regime than in the weak field regime. The results suggest that while these effects are subtle, they provide a potential observational signature of quantum gravity effects. The findings presented here contribute to the broader effort of testing alternative theories of gravity through black hole observations, offering a new perspective on the quantum structure of spacetime at cosmological and astrophysical scales.

Orbital eccentricity in compact binary mergers carries crucial information about the binary's formation and environment. There are emerging signs that some of the mergers detected by the LIGO and Virgo gravitational wave detectors could indeed be eccentric. Nevertheless, the identification of eccentricity via gravitational waves remains challenging, to a large extent because of the limited availability of eccentric gravitational waveforms. While multiple suites of eccentric waveforms have recently been developed, they each cover only a part of the binary parameter space. Here we evaluate the sensitivity of LIGO to eccentric waveforms from the SXS and RIT numerical relativity catalogs and the TEOBResumS-Dali waveform model using data from LIGO-Virgo-Kagra's third observing run. The obtained sensitivities, as functions of eccentricity, mass and mass ratio, are important inputs to understanding detection prospects and observational population constrains. In addition, our results enable the comparison of the waveforms to establish their compatibility and applicability for searches and parameter estimation.

In light of the recently discovered connection between grey-body factors and quasinormal ringing, we derive analytic expressions for the grey-body factors of generic parametrized spherically symmetric and asymptotically flat black holes. These expressions are presented as expansions in terms of the inverse multipole number and the coefficients of the parametrization. The obtained analytic formulas serve as good approximations whenever the deviation from the Schwarzschild geometry is not very large. We demonstrate that the primary parameter determining the grey-body factors is the deviation of the event horizon radius from its Schwarzschild value, while the higher-order coefficients of the parametrization, which govern the near-horizon geometry, are much less significant. This finding is consistent with recent observations that grey-body factors are considerably more stable against small deformations of the near-horizon geometry than quasinormal modes.

In this paper the final stage of the Petrov classification is carried out. As it is known, the Killing vector fields specify infinitesimal transformations of the group of motions of space $V_4$. In the case when in the homogeneous space $V_4$ the group of motions $G_3$ acts simply transitive, the geometry of the non-isotropic hypersurface is determined by the geometry of the transitivity space $V_3$ of the group $G_3$. In this case, the metric tensor of the space $V_3$ can be given by a nonholonomic reper consisting of three independent vectors $\ell_{(a)}^\alpha$, which define the generators of the group $G_3$ of finite transformations in the space $V_3$. The representation of the metric tensor of $V_4$ spaces by means of vector fields $\ell_{(a)}^\alpha$ has a great physical meaning and allows to simplify substantially the equations of mathematical physics in such spaces. Therefore, the Petrov classification should be complemented by the classification of vector fields $\ell_{(a)}^\alpha$ connected to Killing vector fields. For homogeneous spaces this problem has been largely solved. A complete solution of this problem is presented in the present paper, where the Petrov classification for homogeneous spaces in which the group $G_3$, which belongs to type $VIII$ according to the Petrov classification, acts simply transitively, is refined. In addition, the complete classification of vector fields $\ell_{(a)}^\alpha$ for spaces $V_4$ in which the group $G_3$ acts simply transitivity on isotropic hypersurfaces.}

The Laser Interferometer Space Antenna (LISA) is designed to detect a variety of gravitational-wave events, including mergers of massive black hole binaries, stellar-mass black hole inspirals, and extreme mass-ratio inspirals. LISA's capability to observe signals with high signal-to-noise ratios raises concerns about waveform accuracy. Additionally, its ability to observe long-duration signals will raise the computational cost of Bayesian inference, making it challenging to use costly and novel models with standard stochastic sampling methods without incorporating likelihood and waveform acceleration techniques. In this work, we present our attempt to tackle these issues. We adapt ${\tt RIFT}$ for LISA to take advantage of its embarrassingly parallel architecture, enabling efficient analysis of large datasets with costly gravitational wave models without relying on likelihood or waveform acceleration. We demonstrate that we can accurately infer parameters of massive black hole binary signals by carrying out a zero-noise injection recovery using the numerical relativity surrogate model ${\tt NRHybSur3dq8}$. By utilizing all available $m\neq0$ modes in the inference, we study the impact of higher modes on LISA data analysis. We study the impact of multiple massive black hole binary signals in a dataset on the inference of a single signal, showing that the selected source's inference remains largely unaffected. Furthermore, we analyze the LDC-1A and blind LDC-2A datasets from the Radler and Sangria challenge of the LISA data challenges. When eschewing specialized hardware, we find ${\tt NRHybSur3dq8}$ injection-recovery takes approximately $20$ hours to complete, while the analysis of Sangria and Radler datasets takes about $10$ hours to complete.

Quantum Improved Regular Kerr (QIRK) Black Hole is a rotating regular black hole based on the asymptotic safety method. This black hole not only resolves ring singularity and avoids closed timelike curves, but also has well defined thermodynamics. Therefore, it is crucial to find some observable features of this rotating black hole. In this article, we numerically determine the specific parameter range of the QIRK black hole after ensuring the three key properties mentioned above, while investigating its black hole shadow, we find that the extremal QIRK black hole, under a critical angular momentum $a_{\mathrm{cri}}$, can have a similar shadow to the non extremal Kerr black hole. Furthermore, with recent observations from the Event Horizon Telescope (EHT) of Sgr A* and earlier observations of the supermassive black hole M87*, we constrain the QIRK black hole using observational data and explore its potential as an astronomical object.

In this paper we study the Oppenheimer-Snyder (OS) gravitational collapse in the general framework of scale-dependent gravity. We explore the collapse in spherically symmetric solutions suggested both by asymptotically safe gravity (positive $\om$-parameter) and by scale-dependent gravity (negative $\om$-parameter), when a singularity at a finite positive radial coordinate is developed. The inner geometry of the collapsing star is described, as usual, by the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, and matter is uniformly distributed without any assumptions about its equation of state. The outer asymptotically-safe/scale-dependent black hole metric is smoothly matched to the inner geometry, and this yields the equation of motion of the star surface, the energy density, pressure, and equation of state of the collapsing matter. We study in detail the proper-time evolution of the event and apparent horizons. Finally, the constraints of the energy conditions on the equation of state, and its properties, are considered and discussed.

The emergent space paradigm is a unique way to understand the universe's expansion. In this paradigm, as proposed by Padmanabhan in the context of Einstein's gravity the expansion of the universe is driven by the difference between the degrees of freedom on the horizon surface and that within the bulk enclosed by the horizon. This principle called the law of emergence, has been extended to more general gravity theories like Gauss-Bonnet and Lovelock gravity. We derive the law of emergence for braneword models of gravity, starting from the more fundamental and well established principle, the first law of thermodynamics. More specifically, we derive the law of emergence in the context of RS II braneworld, warped DGP model and Gauss-Bonnet braneworld. The significance of the braneworld theory is that the observable universe could be a 3+1 surface or brane embedded in 3+1+d dimensional bulk spacetime. We further compared the derived law with the one proposed by Sheykhi for braneworld models. Our results strongly suggests that the unified first law of thermodynamics is the backbone of the law of emergence.

We develop a perturbation theory for surfaces confining photons and massive particles in static spherically symmetric spacetimes in terms of two parameters: the mass-to-energy ratio and the deviation of metric functions from a given form, e.g., the Schwarzschild solution. Expansions of the gravitational shadow radius in terms of these parameters are constructed up to the second order. The metric expansion in terms of the Schwarzschild mass-to-radius ratio is then reconstructed. Explicit analytical examples of non-standard black hole metrics are considered as an illustration. In some cases perturbative results demonstrate good accuracy even for non-small deviations.

This paper investigates the massive gauge field within spacetime context from a $\mathbb{Z}_2$ quotient of the constant curvature black hole. We investigate how the matter field's back reaction affects the spacetime geometry, considering perturbations in the metric up to the first order. The stress-energy tensor's expectation value can be precisely calculated by evaluating its pull-back onto the covering space. By appropriately selecting boundary conditions for the massive vector field along a non-contractible cycle of the quotient manifold, achieving a negative average energy along a null geodesic becomes feasible, enabling a traversable wormhole.

In this paper, we prove the codimension-one nonlinear asymptotic stability of the extremal Reissner-Nordstr\"om family of black holes in the spherically symmetric Einstein-Maxwell-neutral scalar field model, up to and including the event horizon. More precisely, we show that there exists a teleologically defined, codimension-one "submanifold" $\mathfrak M_\mathrm{stab}$ of the moduli space of spherically symmetric characteristic data for the Einstein-Maxwell-scalar field system lying close to the extremal Reissner-Nordstr\"om family, such that any data in $\mathfrak M_\mathrm{stab}$ evolve into a solution with the following properties as time goes to infinity: (i) the metric decays to a member of the extremal Reissner-Nordstr\"om family uniformly up to the event horizon, (ii) the scalar field decays to zero pointwise and in an appropriate energy norm, (iii) the first translation-invariant ingoing null derivative of the scalar field is approximately constant on the event horizon $\mathcal H^+$, (iv) for "generic" data, the second translation-invariant ingoing null derivative of the scalar field grows linearly along the event horizon. Due to the coupling of the scalar field to the geometry via the Einstein equations, suitable components of the Ricci tensor exhibit non-decay and growth phenomena along the event horizon. Points (i) and (ii) above reflect the "stability" of the extremal Reissner-Nordstr\"om family and points (iii) and (iv) verify the presence of the celebrated "Aretakis instability" for the linear wave equation on extremal Reissner-Nordstr\"om black holes in the full nonlinear Einstein-Maxwell-scalar field model.

We study spherical evolution in scalar-Gauss-Bonnet gravity with additional Ricci coupling and use the gauge-invariant approach of Ref.~\cite{Reall:2021voz} to track well-posedness. Our results show that loss of hyperbolicity when it occurs, is due to the behaviour of physical degrees of freedom. They provide further support to the idea that this behaviour can be tamed by additional interactions of scalar. We also point out a limitation of this gauge-invariant approach: the fact that field redefinitions can change the character of the evolution equations.

Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space wavefunction. The singularities of these cosmological integrals are parameterized by binary hyperplane arrangements. Using different algebraic tools, we shed light on the differential and difference equations satisfied by these integrals. Moreover, we study a multivariate version of partial fractioning of the flat space wavefunction, and propose a graph-based algorithm to compute this decomposition.

Burst searches identify gravitational-wave (GW) signals in the detector data without use of a specific signal model, unlike the matched-filter searches that correlate data with simulated signal waveforms (templates). While matched filters are optimal for detection of known signals in the Gaussian noise, the burst searches can be more efficient in finding unusual events not covered by templates or those affected by non-Gaussian noise artifacts. Here, we report the detection of 3 gravitational wave signals that are uncovered by a burst search Coherent WaveBurst (cWB) optimized for the detection of binary black hole (BBH) mergers. They were found in the data from the LIGO/Virgo's third observing run (O3) with a combined significance of 3.6 $\sigma$. Each event appears to be a BBH merger not previously reported by the LIGO/Virgo's matched-filter searches. The most significant event has a reconstructed primary component in the upper mass gap ($m_1 = 70^{+36}_{-18}\,$M$_\odot$), and unusually low mass ratio ($m_2/m_1\sim0.3$), implying a dynamical or AGN origin. The 3 new events are consistent with the expected number of cWB-only detections in the O3 run ($4.8 \pm 2.1$), and belong to the stellar-mass binary population with the total masses in the $70-100$ M$_\odot$ range.

In this paper we construct a non-perturbative action of the higher spin symmetry algebra on the gravitational phase space. We introduce a symmetry algebroid $\mathcal{T}$ which allows us to include radiation in an algebraic framework. We show that $\mathcal{T}$ admits a non-linear realization on the asymptotic phase space generated by a Noether charge defined non-perturbatively for all spins. Besides, this Noether charge is conserved in the absence of radiation. Moreover, at non radiative cuts, the algebroid can be restricted to the wedge symmetry algebra studied in ArXiv:2409.12178. The key ingredient for our construction is to consider field and time dependent symmetry parameters constrained to evolve according to equations of motion dual to (a truncation of) the asymptotic Einstein's equations. This result then guarantees that the underlying symmetry algebra is also represented canonically.

We propose a two parameters extension of the flat $\Lambda$CDM model to capture the impact of matter inhomogeneities on the background evolution of the Universe. Non virialized but non-linearly evolving overdense and underdense regions, whose abundance is quantified using the Press-Schechter formalism, are collectively described by two effective perfect fluids $\rho_{\rm{c}},\rho_{\rm{v}}$ with non vanishing equation of state parameters $w_{\rm{c,v}}\neq 0$. These fluids are coupled to the pressureless dust, akin to an interacting DM-DE scenario. The resulting phenomenology is very rich, and could potentially address a number of inconsistencies of the standard model, including a simultaneous resolution of the Hubble and $\sigma_8$ tensions. To assess the viability of the model, we set initial conditions compatible to the Planck 2018 best fit $\Lambda$CDM cosmology and fit its additional parameters using SN~Ia observations from DESY5 and a sample of uncorrelated $f\sigma_8$ measurements. Our findings show that backreaction effects from the cosmic web could restore the concordance between early and late Universe cosmological probes.

The near-horizon region of a black hole impacts linear (LP) and circular polarization (CP) through strong lensing of photons, adding large-scale symmetries and anti-symmetries to the polarized image. To probe the signature of lensing in polarimetry, we utilise a geometric model of concentric, Gaussian rings of equal radius to investigate the transition in the Fourier plane at which the photon ring signal begins to dominate over the direct image. We find analytic, closed-form expressions for the transition radii in total intensity, LP, and CP, wherein the resultant formulae are composed of ratios of tunable image parameters, with the overall "scale" set primarily by the thickness of the direct image. Using these formulae, we compute the transition radii for time-averaged images of M87* simulations at 230 GHz, studying both Magnetically Arrested Disc (MAD) and Standard and Normal Evolution (SANE) configurations for various spin and electron heating models. We compare geometric values to radii obtained directly from the simulations through a coherent averaging scheme. We find that nearly all MAD models have a photon ring-dominated CP signal on long baselines shorter than the Earth diameter at 230 GHz. Across favored models for the M87* accretion flow identified by EHT polarimetric constraints, we quantify the sensitivity and antenna size requirements for the next-generation EHT and the Black Hole Explorer orbiter to detect these features. We find that the stringent requirements for CP favour explorations using long baselines on the ground, while LP remains promising on Earth-space baselines.

Primordial black holes can be the entirety of the dark matter in a broad, approximately five-orders-of-magnitude-wide mass range, the ``asteroid mass range'', between $10^{-16}\ M_{\rm Sun}$ -- where constraints originate from evaporation -- and $10^{-11}\ M_{\rm Sun}$ -- from microlensing. A direct detection in this mass range is very challenging with any known observational or experimental methods. Here we point out that, unlike previously asserted in the literature, a transient gravitational wave signal from the inspiral phase of light black hole mergers is in principle detectable with current and future high-frequency gravitational wave detectors, including but not limited to ADMX. The largest detection rates are associated with binaries from non-monochromatic mass functions in early-formed three-body systems.

Recent numerical results seem to suggest that in certain regimes of typical particle velocities the gravitational $N-$body problem (for $3\leq N\lesssim 10^3$) is intrinsically less chaotic when the post-Newtonian (PN) force terms are included, with respect to its classical counterpart that exhibits a slightly larger maximal Lyapunov exponent $\Lambda_{\rm max}$. In this work we explore the dynamics of wildly chaotic, regular and nearly regular configurations of the 3-body problem with and without the PN corrective terms aiming at shedding some light on the behaviour of the Lyapunov spectra under the effect of said corrections. Because the interaction of the tangent-space dynamics in gravitating systems, needed to evaluate the Lyapunov exponents, becomes rapidly computationally heavy due to the complexity of the higher order force derivatives involving multiple powers of $v/c$, we introduce a technique to compute a proxy of the Lyapunov spectrum based on the time-dependent diagonalization of the inertia tensor of a cluster of trajectories in phase-space. We find that, for a broad range of orbital configurations, the relativistic 3-body problem has a smaller $\Lambda_{\rm max}$ than its classical counterpart starting with the exact same initial condition. However, the rest of the Lyapunov spectrum can be either lower or larger in the classical case, suggesting that the relativistic precession effectively reduces chaos only along one (or few) directions in phase-space. As a general trend, the dynamical entropy of the relativistic simulations as function of the rescaled speed of light always has a regime in which falls below the classical value.} We observe that, the sole analysis of $\Lambda_{\rm max}$ could induce possibly misleading conclusions on the chaoticity of systems with small (and possibly large $N$.

The upcoming LISA mission will be able to detect gravitational waves from galactic and extragalactic compact binaries. Here, we report on LISA's capability to probe dark matter around these binaries if the latter constitute black holes. By analyzing the variation in the chirp mass of the binary, we show that depending on the black hole masses, LISA should be able to probe their surrounding dark matter to a luminosity distance of $\approx 1$ Gpc if such binaries are observed within the inner $\approx 10$ pc of their galactic center for particle-like dark matter or near the galactic solitonic core for wave-like dark matter. In the case a null result is recorded during the course of observation of \emph{well-localized} binaries, one can still rule out certain parameter spaces of dark matter as being the dominant contributor to the matter budget of the Universe.

In this work, we approach certain black hole issues, including remnants, by providing a statistical description based on the weak gravity conjecture in the swampland program. Inspired by the Pauli exclusion principal in the context of the Fermi sphere, we derive an inequality which can be exploited to verify the instability manifestation of the black holes via a characteristic function. For several species, we show that this function is in agreement with the weak gravity swampland conjecture. Then, we deal with the cutoff issue as an interval estimation problem by putting an upper bound on the black hole mass scale matching with certain results reported in the literature. Using the developed formalism for the proposed instability scenarios, we provide a suppression mechanism to the remnant production rate. Furthermore, we reconsider the stability study of the Reissner-Nordstrom black holes. Among others, we show that the proposed instabilities prohibit naked singularity behaviors

In this work, we are interested in how spinning effects influence the electronic properties of the graphene wormhole. For this purpose, we have described the graphene by the wormhole background based on the model developed by Gonz\'alez and his co-workers. By applying a coordinate transformation in the metric of graphene wormhole, we can introduce rotating effects. In the continuum limit, by solving the massless Dirac equation in the context of a rotating wormhole background, we obtain the Landau levels for the rotating graphene wormhole. We still have exposed the analogy between the graphene wormhole and fermions on the G\"odel-type spacetime.

We calculate the holographic central charges for general higher curvature gravity theory dual to eight dimensional CFT. To do this, we first elaborate the general form of Weyl anomaly in 8d CFT and find 11 non-trivial linearly independent curvature combinations, one of which is Euler density and the rest are Weyl invariants, including 7 non-differentiated ones and 3 differentiated ones. The Weyl invariants are constructed as invariant polynomials of curvature tensor and covariant derivatives. We denote $W_{(n)}$ as the Weyl invariant that contains a polynormial term with a minimum of $n$ curvature tensors. Interestingly, since there are a total of 12 Weyl invariants in 8d, our finding means two of them are trivial and expressible as total derivatives. The resulting central charges are expressed in terms of 15 theory-dependent constants. Remarkably, we find that the $W_{(2)}$ invariant corresponds to the $c$-charge that is proportional to $C_T$, while the two $W_{(3)}$'s are related to three-point function parameters of energy-momentum tensor. This suggests a possible connection between the $c$-charges of $W_{(n)}$'s and the $n$-point functions of energy-momentum tensor.

We develop a novel holographic dictionary for the thermodynamics of black holes with Lifshitz and hyperscaling violating asymptotics, generalizing the dictionary for Anti-de Sitter black holes. Using our dictionary we show that the holographic Euler equation is dual to a generalized Smarr formula for these black holes, and we find a precise match between the extended bulk and boundary first law. Notably, the dictionary for the central charge appearing in the Euler relation depends on the hyperscaling violating parameter, but not on the Lifshitz dynamical exponent.

Diagrammatic approaches to perturbation theory transformed the practicability of calculations in particle physics. In the case of extended theories of gravity, however, obtaining the relevant diagrammatic rules is non-trivial: we must expand in metric perturbations and around (local) minima of the scalar field potentials, make multiple field redefinitions, and diagonalize kinetic and mass mixings. In this note, we will motivate these theories, introduce the package FeynMG -- a Mathematica extension of FeynRules that automates the process described above -- and highlight an application to a model with unique collider phenomenology.

We explore two-point and four-point correlation functions of a massive scalar field on the flat de Sitter background in the long-wavelength approximation. By employing the Yang-Feldman-type equation, we compute the two-point correlation function up to the three-loop level and the four-point correlation function up to the two-loop one. In contrast to the standard theory of a massive scalar field based on the de Sitter-invariant vacuum, we develop the vacuum-independent reasoning that may not possess de Sitter invariance but results in a smooth massless limit of the correlation function's infrared part. Our elaboration affords to calculate correlation functions of a free massive scalar field and to proceed with quantum corrections, relying only on the known two-point correlation function's infrared part of a free massless one. Remarkably, the two-point correlation function of a free massive scalar field coincides with the Ornstein-Uhlenbeck stochastic process's one and has a clear physical interpretation. We compared our results with those obtained with the Schwinger-Keldysh diagrammatic technique, Starobinsky's stochastic approach, and the Hartree-Fock approximation. At last, we have constructed a renormalization group-inspired autonomous equation for the two-point correlation function. Integrating its approximate version, one obtains the non-analytic expression with respect to a self-interaction coupling constant $\lambda$. That solution reproduces the correct perturbative series up to the two-loop level. At the late-time limit, it almost coincides with the result of Starobinsky's stochastic approach in the whole interval of a new dimensionless parameter $0 \leq \tfrac{\pi^2 m^4}{3\lambda H^4} < \infty$.

We introduce a novel approach for detecting gravitational waves through their influence on the shape of resolved astronomical objects. This method, complementary to pulsar timing arrays and astrometric techniques, explores the time-dependent distortions caused by gravitational waves on the shapes of celestial bodies, such as galaxies or any resolved extended object. By developing a formalism based on that adopted in the analysis of weak lensing effects, we derive the response functions for gravitational wave-induced distortions and compute their angular correlation functions. Our results highlight the sensitivity of these distortions to the lowest frequencies of the gravitational wave spectrum and demonstrate how they produce distinct angular correlation signatures, including null and polarisation-sensitive correlations. These findings pave the way for future high-resolution surveys to exploit this novel observable, potentially offering new insights into the stochastic gravitational wave background and cosmological models.