We construct and analyze a new stationary axisymmetric black hole solution that describes a regular Kerr spacetime immersed in a string cloud background. By employing the non-complexified Newman-Janis algorithm, we generate a rotating metric from a static seed that incorporates both a regularization parameter r_0 and a string density parameter ϵ . The resulting geometry is regular everywhere, possessing a de Sitter-like core that avoids the central singularity. We investigate the thermodynamic stability of this system, revealing a second-order phase transition and the existence of a thermodynamically stable state where Hawking evaporation ceases. Furthermore, we examine the optical properties of the black hole by modeling its shadow as seen by a distant observer. Our results demonstrate a phenomenological decoupling: while the black hole spin primarily governs the geometric distortion of the shadow, the string cloud density acts as a gravitational magnifying lens, significantly increasing the shadow’s angular diameter.suggesting a phenomenological decoupling that could be tested by future interferometric observations.
General Parallel Relativity is a dynamically equivalent formulation of Einstein gravity in which the parallel frame supplies explicit boundary reference data. In this formulation, finite-region energy-momentum and horizon entropy arise as distinct Hamiltonian surface charges. Diffeomorphisms along canonical frame directions define a quasi-local energy-momentum including a matter surface term, while normal-plane boosts at a smooth horizon give entropy. These covariant formulas are applied to the Reissner-Nordström black hole and to a dilatonic charged black hole. In both examples, the matter contribution combines with the Misner–Sharp mass to give the Hamiltonian energy appropriate to the electromagnetic boundary datum. The resulting horizon charges satisfy the thermodynamic relation obtained independently from the Euclidean boundary action.
We investigate Hawking radiation near the thermodynamic critical point of a four-dimensional dilaton black hole with a geometrically deformed angular sector R(r)=(r/r_0)^N . Treating the deformation exponent N as an active control parameter, we locate a second-order phase transition governed by mean-field critical exponents, whose amplitudes are explicitly modulated by N. Solving the Klein–Gordon equation, we derive the exact effective scattering potential and propose a phenomenological Breit–Wigner resonance model for the greybody factor near criticality, motivated by the divergence of thermodynamic response functions. Quasinormal mode analysis in the eikonal limit establishes a correspondence with the unstable photon orbit, and third-order WKB computations of the QNM spectra indicate that N modulates both the ringdown frequency and Lyapunov damping. All thermodynamic, dynamical, and radiative quantities reduce smoothly to the Reissner–Nordström–AdS limit as N → 0^- and α→ 0 . Our results suggest that geometric warping may provide a tunable framework for probing quantum gravitational observables, though direct numerical computation of the greybody factor is required to confirm the predicted resonant enhancement.
In the present paper we consider anisotropic cosmological vacuum solutions in (4 + 1) dimensional general quadratic gravity. In particular, we present a solution with 3 equal and 1 different Hubble parameters, and study its stability. We show that for a certain range of coupling constants this solution is stable. This means that initially totally anisotropic 4-dim Universe can evolve naturally to a product of 3-dim isotropic subspace and 1-dim space. By numerical integration of equations of motion we construct bassin of attraction of this solution which covers part of the initial conditions space with non-zero measure.
We consider the emission of gravitational waves (GW) from a compact binary in a spacetime with compactified extra dimensions. We solve the homogeneous and non-homogeneous wave equation, proving that there is an infinite sum of exponentially decaying pseudo-massive modes which add to the usual one which behaves as 1/r at infinity. We calculate the metric potentials, the equations of motion and the energy flux. We find that in the equations of motion there is a new term at -1PN order. This implies a modification of the energy flux.
This work investigates the thermodynamic and topological properties of rotating black holes (BHs) in Lorentz-violating gravity. By analyzing the Hawking temperature and heat capacity as functions of the horizon radius, we identify second-order phase transitions and clearly distinguish thermodynamically stable regions from unstable ones. To investigate the critical behavior of the system, several thermodynamic geometry formalisms, such as the Ruppeiner, Hendi–Panahiyan–Eslam Panah–Momennia (HPEM), Weinhold, and Quevedo metrics (Cases I and II) are applied. Our analysis reveals that the scalar curvature of HPEM, Ruppeiner, and Quevedo metrics are in excellent agreement with the zeros of heat capacity and successfully capture the phase transition structure of the BH system. Furthermore, we uncover the topological aspects of BH thermodynamics through phase-space diagrams that expose the existence of non-trivial topological structures. BHs can be interpreted as topological defects in the thermodynamic phase space spanned by variables such as temperature and pressure. One can compute the corresponding winding numbers by exploring these defects at both local and global levels and locate a topological charge that takes discrete values +1 , 0, or -1 . Overall, our findings will provide important information about the interplay between thermodynamics, geometry, and topology in rotating BHs within modified gravity theories and may offer valuable constraints on models that incorporate Lorentz symmetry violation.
We determine the small-oscillation period of a simple pendulum in Schwarzschild spacetime. After transients decay, the displaced rope coincides with a geodesic of the induced spatial metric. This determines the radial lift of the bob to quadratic order in the angular amplitude and leads to the period measured by an observer at the bob's equilibrium position, r=r_2, with the fulcrum at r_1, T_(2)=4πr_2^2/c r_s√(N_2(N_1-N_2)), where N_i=N(r_i) and N(r)=√(1-r_s/r) is the Schwarzschild lapse. The result is therefore expressed in terms of the same function that determines clock rates and gravitational redshifts. In the Newtonian limit, we reproduce the classical result T=2π√(L_0/g). We interpret the period close to the horizon in terms of an effective pendulum length. We compare our treatment with the coordinate-length constraint adopted in an earlier study and argue that the two problems are inequivalent away from the classical, weak-field limit.
We study a single-field inflationary scenario with a nontrivial coupling to the Gauss–Bonnet term and compute its predictions for the background dynamics and cosmological perturbations. The model is analyzed within the slow-roll regime, and we derive analytic expressions for the inflationary observables, including the scalar spectral index n_s , the tensor-to-scalar ratio r, and the running α _s . Motivated by string-theoretic considerations, we impose the theoretical constraint V(ϕ )ξ (ϕ ) = constant , which reduces the parameter space and provides a more predictive framework. The Gauss–Bonnet coupling modifies the standard consistency relations and enables compatibility with current Planck constraints for a broad parameter range ( n_s ∈ [0.955, 0.970] , r ∈ [0.003, 0.09] ). We perform a comprehensive Markov Chain Monte Carlo (MCMC) analysis using Planck 2018 and BICEP/Keck data, obtaining posterior constraints on model parameters. Additionally, we examine swampland compatibility, reheating predictions, non-Gaussian signatures, and potential implications for primordial black hole formation. Our analysis demonstrates that this framework provides a well-motivated extension of standard single-field inflation while maintaining observational viability and offering distinctive testable predictions for future cosmological surveys.
The cosmic dynamics of the interacting dark energy is analyzed in the homogeneous and anisotropic spacetime. In particular, the energy exchange mechanism of the dark sector has been studied with the radiation and baryonic matter in the Bianchi I spacetime. The propagation equations of the expansion and shear scalar have been solved to write the mean Hubble parameter. The posterior phase space of the parameters are portrayed by using the latest supernovae type Ia data from Pantheon+SH0ES sample along with the DESI-BAO, CMB and expansion rate data. It is observed that the parameter space of the interacting models are degenerate in the Bayesian approach based MCMC analysis. However, the joint dataset incorporating CMB data may break this degeneracy. The slowing down of cosmic expansion rate appears to be consistent with the observations. The interacting dark energy may provide a mechanism for the anisotropy dissipation. Furthermore, the interacting dark energy may aid partially in relieving the Hubble tension in these models. However, in these varying dark energy models, the extent of anisotropy may be higher as compared to the constant dark energy density model.
This contribution summarizes the state of affairs in the derivation of the Vlasov equations of relativistic kinetic theory of plasma from a microscopic classical physical model of N relativistically moving point charges that interact via classical electromagnetic fields.
A hypersurface anchored variational extension of General Relativity is formulated in which the Einstein-Hilbert action is supplemented by a diffeomorphism invariant functional supported on an embedded spacelike hypersurface whose embedding is varied independently of the spacetime metric. The resulting Euler-Lagrange system consists of the Einstein equations with a localized distributional contribution together with an anchoring equation determining admissible embeddings. For the admissible class of hypersurface functionals considered here, the bulk field equations retain the standard second order principal structure away from the hypersurface and no additional propagating bulk gravitational degrees of freedom are introduced. Under ellipticity and invertibility assumptions, local persistence and linear stability of anchoring hypersurfaces follow from standard implicit function and elliptic estimates. The anchoring condition is generically inequivalent to local slicing gauge conditions and therefore defines a genuine variational restriction rather than a coordinate choice. In the canonical formulation, the momentum constraints retain their standard form, whereas the Hamiltonian constraint acquires a hypersurface supported term. The corresponding smeared generators close in the weak sense: the Dirac algebra is recovered in the bulk, with deviations confined to localized distributional surface contributions. The construction therefore defines a constrained sector of the classical solution space of General Relativity consisting of spacetimes that admit at least one embedded hypersurface satisfying the anchoring equation. In homogeneous cosmology, the localized term induces matching conditions across the anchoring surface, allowing finite transitions in the expansion rate while preserving standard evolution away from the transition hypersurface.
The Laser Interferometer Space Antenna (LISA) is due to launch in the mid-2030s. A key challenge for LISA data analysis is efficient Bayesian inference with parametrised gravitational-wave models, particularly for early inspirals of low- and intermediate-mass black-hole binaries, where time series can contain ∼ 10^8 – 10^9 samples and naive likelihood evaluations become prohibitively expensive. We present a time-domain likelihood-approximation scheme for such signals. The method retains a small subset of samples and defines a modified noise-weighted inner product on this subset that closely reproduces the original inner product on the waveform manifold. Because this alters the effective noise model, the scheme is intended for analysis of simulated, rather than real LISA data. In our examples, the resulting posteriors closely agree with those obtained using much denser sampling, while retaining only 10^3 – 10^4 samples. The computational cost scales linearly with the number of retained samples N_s , so the speed-up is roughly N_f/N_s , where N_f is the original data length; for realistic LISA-like datasets with N_f∼ 10^8 – 10^9 this would correspond to gains of order 10^4 – 10^6 over straightforward frequency-domain likelihood evaluations of the full dataset, although a small number of additional runs is required to verify convergence. The time-domain formulation is particularly convenient for modelling effects naturally expressed through modified time evolution, such as those induced by non-trivial astrophysical environments or additional dynamical fields in beyond-GR theories. This paper provides the theoretical basis for the software package Dolfen.
The null-surface formulation (NSF) is conformally equivalent to general relativity, but the three coupled NSF field equations are challenging to solve. Earlier papers have reported solutions in 2+1 dimensions. This current paper presents a nontrivial exact solution in 3+1 dimensions that is expressed solely in terms of the special “intrinsic” coordinate system of the NSF and the associated angular parameters. To the authors’ knowledge this is the first such solution to be found. The solution is given implicitly, rather than explicitly, but it is nonetheless developed in full. Expressions for the standard geometric constructs—the metric, Ricci, and Einstein tensors—are given explicitly. The Ricci scalar is positive everywhere.
Hyperboloidal foliations which extend to future null infinity are advantageous in extracting gravitation radiation and monitoring the approach to horizon formation. A simple hyperboloidal foliation of the Kerr-Newman family of charged, spinning black hole spacetimes is presented. Its potential application to the simulation of the full range of perturbations of sub-extremal Kerr-Newman black holes is outlined.
We investigate a versatile class of single-field inflationary models governed by a smoothly deformable exponential potential. The potential is characterized by parameters controlling its asymmetry, steepness, and curvature, enabling a continuous interpolation between plateau-like and steep exponential regimes. This flexibility allows the model to exhibit a wide range of inflationary dynamics, including attractor behavior and power-law expansion as emergent features. Within the slow-roll framework, we compute the resulting predictions for the scalar spectral index n_s and the tensor-to-scalar ratio r , and perform a systematic exploration of the parameter space. Our analysis identifies substantial regions consistent with the latest constraints from Planck and BICEP/Keck, demonstrating the model’s capability to describe both low- and high-scale inflation. The inherent adaptability of this framework, along with its connection to exponential and hyperbolic structures, underscores its potential relevance for embedding inflation in high-energy theories.
The region spanning the ring singularity in the Kerr black hole solution is described here as two (flat) discs rather than one. From this viewpoint it follows that the usual depiction of the worldsheet θ =π /2 , ϕ constant (in Boyer–Lindquist coordinates) is missing (multiple copies of) the region r<0 , representable as a triangle in the usual conformal diagram style.
We investigate the excitation of the propagating scalar degree of freedom—the scalaron—in quadratic f(R) gravity by localized Maxwell-Higgs vortices in a (2+1) -dimensional BTZ black hole spacetime. In the perturbative regime where the higher-curvature coupling is small compared to the AdS scale, the modified trace equation reduces to a massive Klein-Gordon equation for the Ricci scalar, sourced by the vortex energy-momentum tensor. Using the Sturm-Liouville structure of the radial operator, we construct the exact radial Green function and obtain the curvature profile for an arbitrary localized source. Outside the vortex core, the induced curvature perturbation exhibits a universal power-law decay R(r) ∼ r^-(1+ν ) , independent of the microscopic vortex structure, where the exponent ν coincides with the standard AdS mass-dimension relation. We demonstrate that the scalar excitation is linearly stable, satisfies the Breitenlohner-Freedman bound, carries finite total energy, and produces exponentially suppressed backreaction on the BTZ geometry, ensuring the smooth recovery of the Einstein limit. These results provide an analytically tractable realization of how higher-curvature corrections activate local gravitational dynamics in three dimensions.
