We consider the holographic description of the dynamical black hole entropy in $f(R)$ higher curvature gravity which proposed by Hollands-Wald-Zhang. On the bulk side, we show that the coarse-grained entropy (outer entropy) of a generalized marginally trapped surface corresponds precisely to the Wald entropy associated with this surface. To get this result, we first formulate the AdS/CFT correspondence in the Einstein frame and derive the correspondence between the von Neumann entropy in the Einstein frame and the $f(R)$ frame. This facilitates the derivation of the correspondence between the two outer entropies in the two frames. Furthermore, we directly derive a focusing theorem associated with generalized expansion in $f(R)$ gravity. We then formulate how to construct the stationary null hypersurface for the generalized expansion and the junction condition to glue a hypersurface in $f(R)$ gravity. Combining these results, we directly derive the expression for the outer entropy in the $f(R)$ frame and identify its holographic dual.

We develop a geometric framework for three-dimensional quantum Hall fluids of extended objects, namely quasistrings, in the presence of a strong three-form background field associated with a bundle gerbe. In the strong-field regime, fast internal dynamics is frozen and the low-energy kinematics is governed by generalized guiding-center variables consisting of vectorial and tensorial coordinates. The resulting reduced bracket is generally shape dependent; however, after projection onto an assumed isotropic gapped internal sector, these guiding-center variables obey a universal noncommutative geometry giving rise to a three-dimensional Girvin-MacDonald-Platzman (GMP)-type algebra for projected density operators. Moreover, we identify a compatible correspondence between this projected algebra and the canonical quantization of a topological $\mathrm{BF}+\mathrm{BB}$ theory at the level of suitably smeared collective operators, with its level taken to be associated with the Dixmier-Douady invariant. Our results provide a kinematic starting point for investigating incompressible quantum Hall-type phases and their geometric and topological features in three spatial dimensions.

In this paper, we investigate the generation of gravitational waves (GWs) from a first-order QCD confinement-deconfinement phase transition under an external magnetic field from holography. We analyze the GW spectra across both hard-wall and soft-wall models for Jouguet detonations and nonrunaway scenarios. Our results indicate that increasing the magnetic field shifts the spectral peak to lower frequencies. The predicted GW signals are potentially detectable by observatories such as IPTA, SKA, BBO, and NANOGrav. Decomposing the spectra reveals that sound waves typically dominate the signal around the peak frequency, bubble collisions prevail at spectral extremities, and the contribution from magnetohydrodynamic turbulence is significant only for nonrunaway bubble scenarios at high frequencies. This work suggests that magnetized QCD phase transitions are viable cosmological sources for observable GW backgrounds, offering a potential pathway to constrain primordial magnetic fields through future pulsar timing array observations.

For over four decades, Gribov’s no-pole condition has been almost exclusively explored in Euclidean space, where the elliptic nature of the Faddeev-Popov operator provides a clear spectral boundary. In physical Minkowski spacetime, however, this operator becomes a hyperbolic wave operator, and the Euclidean positivity criterion collapses. We show that the natural Lorentzian replacement is a real-time boundary-value problem: a gauge configuration remains inside the first Gribov region as long as the Faddeev-Popov wave equation admits no source-free solutions obeying the Feynman boundary condition. For backgrounds localized in time, this condition translates to the injectivity of the negative-frequency block of the classical ghost scattering map. For stationary backgrounds, it becomes a spatial bound-state or threshold-resonance problem under Fourier transformation. Using a Wronskian identity, we prove that pure frequency mixing in stable self-adjoint time-dependent channels is structurally protected and cannot by itself produce the obstruction. While static chromomagnetic backgrounds reproduce the familiar zero-frequency horizon crossing, static chromoelectric potentials reach the horizon at finite, nonvanishing frequency—a uniquely Lorentzian phenomenon arising because $A_0$ couples directly to the ghost time derivative. We also cast the condition in Fredholm form and show that the exact restriction is a functional determinant, which the naive local continuation of the Gribov-Zwanziger action fails to reproduce, leaving the construction of a genuine local real-time action as the central open problem.

Extensive systems have a simple thermodynamic signature; the dimensionless canonical free energy scales homogeneously with the size of the system. We show that the failure of this scaling, measured by the replica energy $\mathcal{E}$, provides a useful bridge between statistical mechanics and quantum field theory. The associated differential operator $(1-\frac{1}{d}L{\partial }_L)$ removes the leading bulk contribution to $\mathcal{F}=\beta F_{\mathrm{can}}=-\log Z$ and isolates the part that is sensitive to boundaries, topology, defects, long-range forces, or other sources of nonadditivity. In quantum field theory this thermodynamic idea has two closely related uses. For ordinary finite-volume or spherical partition functions, suitable higher-order versions of the same filter remove local counterterms and extract universal fixed-point data such as the central charge, the sphere free energy $F$, and the Euler anomaly coefficient $a$. For replica geometries with entangling defects, the same filtering principle gives the renormalized defect free energy. In $2+1$ dimensions, its $n\to 1$ limit gives the entropic $F$-function, with the sign fixed below by the standard free-energy convention. We use this perspective to distinguish ordinary finite-size corrections, topology-dependent constants in gapped phases, subextensive fracton degeneracies, and genuinely nonextensive systems with long-range interactions such as self-gravitating thermal matter. Replica energy therefore offers a common thermodynamic language for additivity, defect free energies, and renormalization-group irreversibility.

It has been claimed in a series of papers that scalar fields with a fourth-order $\mathrm{Lagrangian}\sim (\square \phi {)}^2$ can solve the cosmological constant problem by canceling the loop contributions from standard model fields, and that their fluctuations can be the source of the primordial density perturbations of the Universe, without the need for inflation. We dispute these claims. The spectrum of the theory includes a ghost, which leads to classical instabilities and quantum violation of unitarity. We show that the new scalar particles cannot cancel the standard model contributions to the cosmological constant, unless they include a unitarity-violating ghost at the quantum level. Further, the coupling of such scalars to the particles of the standard model induces a confining fifth force which rules it out as a source of density perturbations in the early Universe.

We uncover a “junction law” for genuine multipartite entanglement, suggesting that in gapped local systems multipartite entanglement is controlled and effectively localized near junctions where subsystem boundaries meet. Using the Rényi-2 genuine multientropy ${\mathrm{GM}}_2^{(\mathtt{q})}$ as a diagnostic of genuine $\mathtt{q}$-partite entanglement, we establish this behavior in ($2+1$)-dimensional gapped free-fermion lattices with correlation length $\xi$. For partitions with a single junction, ${\mathrm{GM}}_2^{(\mathtt{q})}$ exhibits a universal scaling crossover in $L/\xi$, growing for $L\lesssim \xi$ and saturating to a $\xi$-dependent constant for $L\gg \xi$, up to $\mathcal{O}(e^{-L/\xi })$ corrections. In sharp contrast, for partitions without a junction, ${\mathrm{GM}}_2^{(\mathtt{q})}$ is exponentially suppressed in $L/\xi$ and drops below numerical resolution once $L\gg \xi$. We observe the same pattern for $\mathtt{q}=3$ (tripartite) and $\mathtt{q}=4$ (quadripartite) cases, and further corroborate this localization by translating the junction at fixed system size. We also provide a geometric explanation of the junction law in holography. Altogether, these results show that in this gapped free-fermion setting genuine multipartite entanglement is localized within a correlation length neighborhood of junctions.

How many canonical degrees of freedom are dynamically needed to reproduce the Hamiltonian evolution of a regulated field theory? We address this question for a UV/IR-regularized classical scalar field by identifying the minimal symplectic dimension required to reproduce a single trajectory by an autonomous Hamiltonian system. Using symplectic model order reduction as a structure-preserving diagnostic, we show that, for the free scalar field, this dimension is controlled not by the volume-extensive number of regulated field modes but by the smaller number of distinct normal-mode frequencies below the ultraviolet cutoff. In a flat cubic box, this gives an area-type scaling with the size of the region, up to slowly varying corrections. For geodesic balls in maximally symmetric curved spaces, positive curvature produces a superarea enhancement that remains subextensive, while negative curvature suppresses the scaling, with the flat result recovered smoothly in the small-curvature limit. Numerical experiments indicate that the same frequency-based mechanism persists in weakly interacting $\lambda {\varphi }^4$ theory on quasi-integrable timescales. Beyond the counting result, the reduced dynamics has a characteristic algebraic structure: it decomposes into independent oscillator blocks, while reconstructed field modes are linear combinations of these blocks and have Poisson brackets governed by a projector rather than the identity. In this precise classical sense, overlapping degrees of freedom arise dynamically, without modifying the canonical structure by hand. The results provide a controlled setting in which area-type dynamical scaling and overlap structures can be studied before quantization and help separate ordinary Hamiltonian compression effects from genuinely gravitational mechanisms.

The formation of a cusp on a black hole shadow is a striking signature of physics beyond the Kerr paradigm. Using the Konoplya-Zhidenko metric, a general parametrized deformation of the Kerr black hole, we demonstrate that this morphological change fundamentally alters the shadow’s topology with the topological charge flipping from 1 to $-1$. To analyze this topological transition, we introduce a gravitational equal-area law, analogous to Maxwell’s construction in thermodynamics, and identify a critical point for cusp formation. Near this point, we uncover universal behavior characterized by a critical exponent $1/2$, which places this gravitational lensing system within the mean-field universality class. These results establish a new framework for testing fundamental physics of black hole shadows, reframing the search for deviations from general relativity as a targeted hunt for a distinct topological and critical phenomenon.

We numerically construct a family of stationary, axisymmetric black hole solutions in Einstein-Born-Infeld theory, incorporating both electric charge and rotation. Our results indicate that when nonlinear electromagnetic effects are weak, rotating BI black holes with fixed spin approach the extremal limit as the electric charge increases. In contrast, strong nonlinear effects lead to the termination of solutions at configurations corresponding to naked singularities. We demonstrate that nonlinear electrodynamics enhances the gyromagnetic ratio relative to that of Kerr-Newman (KN) black holes. Additionally, we analyze the innermost stable circular orbits (ISCOs) and find that both prograde and retrograde ISCO radii are consistently smaller than those found in KN black holes.

Gravitational models with nonminimal couplings involving functions of the matter Lagrangian and curvature have become popular in recent decades. By coupling the matter Lagrangian directly to the gravitational Lagrangian, one hopes to construct theories that can explain dark energy or dark matter without introducing additional sources. When this matter Lagrangian describes a perfect fluid, some technicalities are involved in its variational formulation. We present a careful derivation of the gravitational field equations together with the complete set of fluid equations using two approaches: Schutz’s velocity potential and Brown’s Lagrange multipliers. We find that with nonminimal couplings, the energy-momentum conservation equations give rise to a nonvanishing contribution which acts in a different direction depending on the approach. This also leads to the emergence of different effective thermodynamic quantities such as the number density, chemical potential, free energy, and temperature. We demonstrate the nonequivalence of the Lagrangian formulations of Schutz and Brown for these types of models and provide a detailed interpretation of our results.

In a very recent paper, we computed the quasibound states of massless acoustic excitations interacting with a new (effective) acoustic geometry with circulation. Notably, the behavior of this acoustic black hole aligns with the phenomenology observed in recent experiments that include superfluids. Such vortex fluid flow bundles exhibit solid-body rotation at length scales larger than the inter-vortex distance, which adds some complexity to the study of quantum fluid behavior. To theoretically deal with this issue, we present an extension of our previous results by including a solid-body rotation term at the angular fluid velocity and then we perform a spectral study by using the analytical solutions for the scalar wave equation of motion. The resulting analytically solvable framework bridges idealized acoustic black-hole models and experimentally motivated rotating-fluid configurations, providing a more realistic description of quasibound state spectra in analog gravity.

gwNRHME is a framework that converts multimodal (i.e., containing several spherical harmonic modes) quasicircular waveforms into their eccentric counterparts, provided the quadrupolar eccentric mode is known, by exploiting universal eccentric modulation functions. Leveraging this framework, we combine the quasicircular numerical relativity (NR) surrogate model NRHybSur3dq8 with the quadrupolar, nonspinning, eccentric surrogate NRSurE_q4NoSpin_22 to construct a multimodal, nonspinning, eccentric model, denoted as gwNRHME_NRSur_q4, which includes nine modes: $(2,\{1,2\})$, $(3,\{1,2,3\})$, $(4,\{2,3,4\})$, and (5, 5). When compared against 156 eccentric Simulating eXtreme Spacetimes NR waveforms, gwNRHME_NRSur_q4 achieves median frequency-domain mismatches (computed using the Advanced LIGO design sensitivity) of $\sim 9\times {10}^{-5}$, with a standard deviation of $\sim 2\times {10}^{-4}$. To demonstrate the modularity of the framework, we further combine NRSurE_q4NoSpin_22 with effective-one-body models SEOBNRv5HM and TEOBResumS-Dali in their nonspinning limits, yielding eccentric waveforms with median mismatches of $\sim 2\times {10}^{-4}$ and $\sim {10}^{-3}$, respectively, with standard deviation of $\sim 2\times {10}^{-3}$ and $\sim 2\times {10}^{-2}$, respectively. Finally, we provide both a surrogate model, gwEccEvolve_q4NoSpin_Sur, and an analytical model, gwEccEvNSv2, for the eccentricity evolution up to $2M$ before merger, based on eccentricity definitions derived from the universal modulation functions. The gwNRHME framework is publicly available through the gwModels package, and the resulting waveform models will be released via the gwsurrogate package.

We derive an obstruction to Friedmann–Lemaître–Robertson–Walker (FLRW) daughter cosmologies from static, asymptotically flat regular black holes. The trapped region of such a parent is Kantowski–Sachs rather than FLRW, so the daughter must be introduced as a separate matched region. For closed daughters, the angular Darmois condition is controlled by the Misner–Sharp mass: asymptotic flatness and finite Arnowitt–Deser–Misner mass force the induced density to decay as $A^{-3}$, while the $k=+1$ curvature term scales as $A^{-2}$. The minimal closed branch is therefore bounded rather than indefinitely expanding. Flat and open daughters avoid this boundedness mechanism. For their maximal homogeneous FLRW continuations, the regular-end affine-averaged null energy condition (ANEC) theorem excludes simultaneous nonstaticity, curvature regularity, null geodesic completeness, and ANEC consistency. For Bardeen, the parent source does not naturally supply the late-time support needed for an unbounded closed daughter. Within these criteria, a viable FLRW daughter therefore requires additional structure, such as modified asymptotics, nonminimal matching, non-FLRW evolution, or an additional stress-energy component.

Spontaneous scalarization provides a dynamical mechanism to evade the no-hair paradigm, but it has been argued to generically eliminate the Cauchy horizon in charged black holes. We show that this obstruction is not universal, but instead follows from the sign-definite structure of the Einstein-Maxwell source term. Within the $P$-dual formulation of nonlinear electrodynamics, we derive a general condition under which the effective scalar source changes sign between the horizons, allowing the integral constraint to be satisfied without destroying the Cauchy horizon. This establishes that the fate of the Cauchy horizon depends on the electromagnetic coupling and identifies candidate theories where scalarized horizons may persist. The resulting framework opens the possibility of studying scalarization in the interhorizon region and its interplay with mass inflation.

Direct detections of gravitational waves provide a unique opportunity to probe the astrophysical origin of compact binary mergers. The formation channels of these systems remain highly debated, and a fraction may originate in dynamical environments or active galactic nuclei. Binaries formed in such environments are expected to experience line-of-sight acceleration from their surroundings, which can imprint characteristic signatures on the observed gravitational wave signal. Here, we rederive the line-of-sight acceleration effects and implement them in state-of-the-art quasicircular waveform models with precession and higher-order modes. We also implement the corrections in eccentric waveform models, applying them consistently to all contributing harmonics. Using this model, we investigate the impact of these effects on the inference of line-of-sight acceleration and analyze several selected events from the Gravitational-Wave Transient Catalog observed during the third observing run of LIGO and Virgo. We find no substantial evidence for line-of-sight acceleration in these events. We also show that an inconsistent treatment of line-of-sight acceleration between higher harmonics can lead to biased conclusions. Our model provides a robust framework for uncovering line-of-sight acceleration in current and future gravitational wave observations, enabling more accurate probes of environmental signatures in compact binary formation.

The Event Horizon Telescope (EHT) imaging of the central objects in the M87 and Milky Way galaxies provides compelling evidence that these objects are consistent with (Kerr) black holes. In view of these observations and the future expectations of very long baseline interferometry (VLBI) on which the EHT observations are based, an intensive research work has been carried out in the literature simulating light trajectories and reconstructing the corresponding optical appearance for a wide array of modified black holes and ultracompact objects. The corresponding images are directly affected not only by the background spacetime geometry but also by the physics of the accretion disk, whose combination yields a characteristic fingerprint. In this paper, we consider such a fingerprint for objects which are not asymptotically flat but instead approach an anti–de Sitter spacetime. This assumption significantly influences light trajectories and, consequently, the corresponding images of the objects as seen by an observer at some distance, which can be used in future VLBI observations for testing alternatives of this kind to the Kerr paradigm. We illustrate our considerations with the examples of a Schwarzschild–anti–de Sitter black hole and a black string, discussing their most notable departures from canonical, asymptotically flat black hole spacetimes.

We develop a unified framework for testing gravity beyond general relativity (GR) with continuous gravitational waves (CWs) from individual supermassive black hole binaries. These long-lived, nearly monochromatic nanohertz signals offer unique strengths for precision tests of gravity, since their coherent phase evolution and inter-pulsar correlations in pulsar timing arrays (PTAs) retain detailed information about departures from GR over cosmological propagation distances. We consider three representative classes of deviations from GR: additional polarization states, modified dispersion relations, and parity-violating birefringence. For each, we derive the interpulsar cross-correlation, the modified antenna response, and the propagation-induced pulsar-term phase delay. For nontensorial polarizations, the CW cross-correlation scales linearly in the alternative-polarization amplitude, compared to the quadratic scaling of the gravitational-wave background, provided the beyond-GR modes are subdominant. PTAs are also competitive for modified dispersion relations, where low frequencies enhance both the antenna-pattern modification and the pulsar-term phase delay. Birefringence, by contrast, is suppressed at nanohertz frequencies for most parity-violating theories. We validate the framework with injection-and-recovery simulations for breathing-mode and massive-graviton signals at current observational limits, recovering the injected beyond-GR parameters and distinguishing the CW signal from both correlated and uncorrelated background models. We further show that a pure-GR CW template recovers source parameters without significant bias when beyond-GR physics is present in the data, supporting a two-stage analysis strategy: identify candidates under GR, then test for deviations.

Dynamical dark energy theories generically introduce a time-dependent field that causes the accelerated expansion of the Universe on large scales. When embedding black hole solutions in such a cosmological spacetime, this time dependence naturally gives rise to cosmological hair; i.e. the local black hole physics is no longer controlled by just the mass and spin of the black hole but also impacted by the dark energy field. However, known such solutions are unstable. Focusing on the cubic Galileon as a concrete and illustrative example, we discuss the restrictions imposed on physical solutions by their regularity and stability in detail. We explicitly derive solutions that both recover the desired cosmological long-range behavior and give rise to well-behaved, regular and stable, short-range dynamics around black holes. We show how the nature of the scalar hair around these local black hole solutions encodes cosmological information, highlighting novel and tantalizing prospects of directly probing cosmological dynamics with black hole observations.

Reducing orbital eccentricity in numerical relativity simulations of binary black holes is essential for producing astrophysically relevant gravitational wave models, as many of these systems are expected to be near circular in nature. Standard eccentricity-reduction procedures rely on iterative schemes, often requiring four or more trial simulations to achieve desired thresholds. This approach is computationally expensive because each trial simulation adds $\sim 10\%$ to the total simulation run-time of multiple weeks to months. We introduce a data-driven approach that accelerates this process by learning the values of the initial orbital frequency, ${\mathrm{\Omega }}_0$, and radial velocity, ${\dot{a}}_0$, that yield an evolution with small eccentricity. This is done using a Gaussian process regression model trained on an archive of previously eccentricity-reduced numerical relativity simulations. For all configurations tested, using the trained model consistently reduces the number of required eccentricity-reduction iterations to just zero or one, significantly lowering computational costs relative to post-Newtonian initial guesses. These results demonstrate the power of data-driven methods in accelerating expensive numerical relativity simulations.