This paper presents a study on gravitational vacuum stars (gravastars) with an isotropic matter distribution in de Rham-Gabadadze-Tolley (dRGT) massive gravity incorporating Buchdahl metric function. Here we have conducted an analysis on thin-shell singularity-free gravastar configuration. The study demonstrates the viability of gravastars as alternatives to black holes (BHs) in this massive gravity. Our research yields singularity free analytical solutions for gravastar interior and without event horizon. Our discussion focuses on the properties of the thin shell of ultra-relativistic stiff fluid viz., length, energy, entropy and the massive gravity’s impact on these physical properties. The junction conditions have been carefully examined and study of surface redshift analysis implies regularity of the model. Our investigation also includes energy condition analysis supporting the thin shell formation. Thus our solutions eliminate singularities and information paradoxes and the implications of these solutions are seemingly noteworthy and exhibit physical desirable properties.

In this paper, we study thermodynamics and its applications of a family of static charged dilaton black holes in 2+1 dimensions found by Chan and Mann [1] and Xu [2]. There is a dimensionless parameter [Formula: see text] in the black hole solutions presented: it is related to the coupling constant for the dilaton with the electromagnetic field and the gravitational field. Black hole horizons exist only for [Formula: see text]. [Formula: see text] black hole is a solution to low energy string theory. Thermodynamics is studied in the canonical ensemble where charge is constant as well as in grand canonical ensemble where the potential is constant. The cosmological constant is considered as a thermodynamical variable where the pressure [Formula: see text]. We computed the first law and the Smarr relations for the black hole and introduced two new thermodynamical parameter in order to satisfy the first law. We computed temperature, thermodynamic volume, specific heat capacities, Gibbs free energy and studied local and global stability of the black hole. Thermodynamic volume differs from the geometric volume. In the canonical ensemble, we noticed that thermodynamic behavior falls into two broad categories: For [Formula: see text], small black holes are locally stable and large black holes are not. For [Formula: see text] the black hole is locally and globally stable for all values of the horizon radius. In order to demonstrate the two broad categories, we have presented [Formula: see text] and [Formula: see text] black holes in detail. There were no phase transitions for the above values of [Formula: see text]. In the grand canonical ensemble, we noticed that there is a Hawking-Page phase transition for the black hole with [Formula: see text]. We have also studied the Joule-Thomson expansion and the Reverse Isoperimetric Inequality of these black holes. We made the observation that the charged dilaton black hole does not violate the Reverse Isoperimetric Inequality for certain values of the parameters of the theory. Finally, we have suggested future work.

In this work, we explored the dynamics of black holes within the framework of Kalb-Ramond gravity, emphasizing the effects of spontaneous Lorentz symmetry breaking on their perturbative and thermodynamic properties. Starting with a modified spherically symmetric black hole solution, we derived and analyzed the spin-dependent Regge-Wheeler potentials for scalar, vector, and tensor perturbations, uncovering significant deviations from the Schwarzschild black hole due to the Lorentz symmetry-breaking parameter. Our findings revealed that the parameter strongly influences the stability of the black hole and the propagation of perturbative modes. Additionally, we calculated GFs to investigate the transmission coefficients of black hole radiation and demonstrated their dependence on both the spin of the fields and the symmetry-breaking effects. Thermodynamic analyses showed modifications to the temperature, entropy, and specific heat, which highlighted the critical role of Lorentz symmetry-breaking effects on black hole stability. Furthermore, we discussed the area quantization of the black hole horizon, revealing its direct dependence on the symmetry-breaking parameter and providing insights into the quantum nature of black holes. These results collectively enrich our understanding of black hole physics under modified gravity theories and offer potential observational implications.

Abstract Restricted by event horizon suppression, tidal disruption events (TDEs) provide a unique window into otherwise hidden supermassive black holes (SMBHs) at the lower end of the mass spectrum, allowing the connection between star formation and SMBH mass to be explored across a broad stellar mass range. We derive stellar masses and specific star formation rates using Prospector fits to UV–mid-infrared broadband spectral energy distributions (SEDs) for 42 TDE hosts, together with a high-mass comparison sample, and combine these with SMBH mass estimates from the literature. We first verify our approach by reproducing the established result that quenched galaxies host more massive SMBHs than star-forming systems at fixed stellar mass, a result widely interpreted as evidence for SMBH growth driving the blue-to-red sequence transition. However, examining the TDE sample in isolation reveals a trend reversal at lower masses, uncovering a surprising population of low-mass (10 9.6 ≲ M gal ≲ 10 10.5 M ⊙ ), quenched galaxies hosting SMBHs systematically less massive ( M BH ≲ 10 6.5 M ⊙ ) than those in star-forming galaxies of comparable stellar mass. After ruling out degeneracies in our SED fits, we conclude that this reflects a physical difference in the quenching mechanism between these TDE hosts and the more massive galaxies. This is unlikely to be driven by active galactic nucleus feedback, and could instead result from environmental processes, which can end star formation and hinder SMBH growth. We also show that the quenched and poststarburst population within the TDE sample is likely underrepresented due to selection biases, suggesting the true fraction could be even higher than observed.

In the present work, several mysteries of a black hole, including its spinning speed, frequency, angular momentum, and rotational kinetic energy, could be addressed. Indeed, the radius, density, surface temperature, thermal energy, and rotational speed of a black hole singularity and the accretion disc may be increased and decreased rapidly according to the conservation law of angular momentum and energy. The transitional and rotational kinetic energy of particles in an accretion disc of a black hole is thermalized. The Nuclear fusion ball has been squeezed steeply due to the higher pressure of a black hole to produce a new superparticle. The Gas and dust particles are capable of spinning up quickly to orbit the black hole at a huge speed and momentum. An accretion disc of a black hole could be distorted and heated up by the black hole singularity, superparticles, and celestial objects. The Powerful gravitational waves of a black hole singularity propagated through an event horizon and an accretion disc of a black hole to make ripples. The turbulent superparticles can travel through the event horizon and accretion disc of a black hole to ripple, and tear apart the gas and dust particles or make powerful black hole jets due to their motion throughout a black hole’s accretion disc. Celestial objects are mostly responsible for the tidal disruptions of a black hole. The radius of a black hole singularity had been compressed and reduced to the size of an atom due to its mass and gravitational pressure. Otherwise, the thermal energy and superparticle degeneracy pressure would suspend the distortion and reduction of a singularity ball. The hydrostatic balance of a black hole singularity protected it from any further collapsing and evaporation.

Abstract This paper analyzes photon orbits around a rotating black hole in Einstein-Bumblebee gravity, where Lorentz symmetry is broken. We solve the Hamilton-Jacobi equation to model the photon motion, which shows significant deviations from predictions of general relativity. A key finding is a critical inclination angle that determines the number and position of photon orbits. All orbits outside the event horizon are unstable. Importantly, the critical impact parameter decreases with stronger Lorentz violation, providing a potential observational test to distinguish this theory from standard gravity.

In four-dimensional vacuum general relativity the only known static, exact and analytical black hole solution is given by the Schwarzschild spacetime. In this paper this renowned metric is generalized by adding another integrating constant, a hair that switches the metric from the Petrov type D to the type I . This new parameter represents the intensity of an external gravitational field, which can be considered the hyperbolic generalization of the Witten’s bubble of nothing. No curvature or conical singularities are present outside the event horizon. The no hair arguments are circumvented because the metric is not asymptotically flat, and neither is the black hole spherical. The gravitational hair continuously deforms the Schwarzschild geometry: the horizon becomes oblate, while its area is reduced. Conserved charges and thermodynamic properties of the black hole are studied.

Abstract In this work, we demonstrate that the hyperboloidal foliation technique, applied to the study of black hole quasinormal modes, where the spatial boundary is shifted from spacelike infinity to the future event horizon and null infinity, is effectively equivalent to the continued fraction approach, in which the asymptotic wave function typically diverges at both ends of spatial infinity. Specifically, a given hyperboloidal slicing, corresponding to a particular choice of coordinates, always uniquely determines a scheme for extracting the asymptotic form of the wave function at the spatial boundary. Owing to the mathematical equivalence, it follows that the efficiency and precision observed using the hyperboloidal approach should be attributed, not to avoiding the pathological behavior at the spatial boundaries, but primarily to other factors, such as the use of Chebyshev grids.

In this paper I present a case study of the creation of the Event Horizon Telescope (EHT), which provided the first image of a black hole shadow (April 2019) and that of the central black hole of the Milky Way (May 2022), as one in which the collaborative approach was primarily motivated by strong epistemic needs. To this end, I introduce and explore the notion of "epistemic constraint," meaning any component of the world that prevents us from gaining some definite kind of knowledge in a specific manner and allows or promotes some other specific kind of knowledge in defined ways. The collaborative approach that led to the recent images of black hole shadows through the EHT is described in terms of "epistemically constrained collaboration" - i.e., a collaborative mode of research where the epistemic constraints prevail over other factors - and the most important features of this concept are expounded.

Abstract The main goal of this work is to investigate how relevant quantum gravity corrections can be, at an effective level, in the geometry describing the exterior of a black hole, and whether such corrections can be tested observationally. For this purpose, we employ Bozza's method to calculate the deflection angle of light in presence of the strong gravitational field generated by an improved Schwarzschild-like black hole whose metric, regular throughout the entire spacetime, was derived using the improved Generalized Uncertainty Principle (GUP). This framework incorporates effective quantum gravity corrections that resolve the physical singularity inside the black hole, quantified by a model parameter | Qc |. In addition, the event horizon, the photon sphere, and the shadow radius receive modifications characterized by a second model parameter Qb . Using observational properties of the supermassive black holes Messier 87* and Sagittarius A * reported by the Event Horizon Telescope, we derive constraints on the parameter | Qb |, namely 0 ≤ | Qb | ≤ 0.3. To the best of our knowledge, these are the first constraints reported in the literature for this improved GUP parameter. Since | Qc | does not play a significant role in the correction of the shadow radius, it was not possible to impose restrictions on its allowed values, however, it is important to consider a non-zero | Qc | in order to avoid a black hole singularity.

Abstract Within a framework requiring a well-defined event horizon and matter obeying the weak energy condition, we employ gravitational decoupling method to construct non-singular hairy black holes: spherically or axially symmetric. These solutions arise from a deformation of the Minkowski vacuum, where the maximum deformation can yield the Schwarzschild metric for the static case, and the Kerr geometry for the stationary case, respectively.

We investigated an exact solution in a conformal invariant Randall-Sundrum 5D warped brane world model on a time dependent Kerr-like spacetime. The singular points are determined by a quintic polynomial in the complex plane and fulfills Cauchy’s theorem on holomorphic functions. The solution, which is determined by a first-degree differential equation, shows many similarities with an instanton. In order to describe the quantum mechanical aspects of the black hole solution, we apply the antipodal boundary condition. The solution is invariant under time reversal and also valid in Riemannian space. Moreover, CPT invariance in maintained. The vacuum instanton solution follows from the 5D as well as the effective 4D brane equations, only when we allow the contribution of the projected 5D Weyl tensor on the brane (the KK-‘particles’). The topology of the effective 4D space of the brane is the projective RP3 (elliptic space) by identifying antipodal points on S3. The 5D is completed by applying the Klein bottle embedding and the Z2 symmetry of the RS model. This model fits very well with the description of the Hawking radiation, which remains pure. We have also indicated a possible way to include fermions. Our 5D space admits a double cover of S3 and after fibering to the S2, we obtain the effective black hole horizon. The connection with the icosahedron discrete symmetry group is investigated. It seem that Bekenstein’s conjecture that the area of a black hole is quantized, could be applied to our model.

Abstract We study synchrotron polarization in spatially resolved horizon-scale images, such as those produced by the Event Horizon Telescope (EHT). In both general relativistic magnetohydrodynamic (GRMHD) simulations and simplified models of the black hole magnetosphere, the polarization angle, quantified by the complex observable ∠β 2 , depends strongly and systematically on the black hole spin. This relationship arises from the coupling between spin and the structure of the magnetic field in the emission region, and it can be computed analytically in the force-free limit. To explore this connection further, we develop a semianalytic inflow framework that solves the time-stationary axisymmetric equations of GRMHD in the black hole’s equatorial plane; this model can interpolate between the force-free and inertial regimes by varying the magnetization of the inflow. Our model demonstrates how finite inertia modifies the structure of the electromagnetic field and can be used to quantitatively predict the observed polarization pattern. By comparing reduced models, GRMHD simulations, and analytic limits, we show that the observed synchrotron polarization can serve as a robust diagnostic of spin under assumptions about Faraday rotation and the emission geometry. Applied to EHT data, the model disfavors high-spin configurations for both M87 ∗ and Sgr A ∗ , highlighting the potential of polarimetric imaging as a probe of both black hole spin and near-horizon plasma physics.

Abstract The spherical geodesics of a neutral massive particle around Kerr-Newman black holes are investigated. The radii of these orbits generally satisfy a quintic polynomial equation with four dimensionless parameters, i.e. the spin u and charge w of the black hole and the conserved angular momentum β and conserved energy γ of the particle. For the γ = 1 case, we obtain analytical expressions of the radii for the polar, equatorial and general orbits. In the (u, w, β) space, a no-orbit surface is found. When the parameters lies on this surface there is no orbit outside the event horizon, otherwise one unstable orbit exists outside the event horizon. For polar orbits with 0 < γ < 1, a boundary surface in (u, w, γ) space is identified which determines the existence of polar orbits outside the event horizon. For polar orbits with γ > 1, there is always one unstable orbit outside the event horizon. For equatorial orbits with 0 < γ < 1, in each rotating case (prograde and retrograde case), a boundary surface in (u, w, γ) space is identified which divides the parameter space into two regions: one region with two orbits (one stable and the other unstable) and the other with no orbit outside the event horizon. Parameters on the boundary surface correspond to ISCOs. An analytical formula for the ISCOs is derived by choosing (w, γ) as independent variables. For equatorial orbits with γ > 1, one unstable orbit always exists outside the event horizon. The radial stability of the various orbits outside the event horizon is also discussed.

A bstract The Carrollian limit ( c → 0) of General Relativity provides the geometric language for describing null hypersurfaces, such as black hole event horizons and null infinity. Motivated by the well-established electric and magnetic limits of Galilean electromagnetism, we perform a systematic analysis of the low-velocity limit of linearized gravity to derive its Carrollian counterparts. Using a 1+3 covariant decomposition, we study the transformation properties of linear tensor perturbations (gravitational waves) on a Friedmann-Lemaître-Robertson-Walker background under Carrollian boosts. We demonstrate that, analogous to the electromagnetic case, the full set of linearized Einstein’s equations is not Carrollian-invariant. Instead, the theory bifurcates into two distinct and consistent frameworks: a Carrollian Electric Limit and a Carrollian Magnetic Limit . In the electric limit, dynamics are frozen, leaving a static theory of tidal forces ( E ab ) constrained by the matter distribution. In contrast, the Magnetic Limit yields a consistent dynamical theory where the magnetic part of the Weyl tensor ( H ab ), which governs gravito-magnetic and radiative effects, remains well-defined and is sourced by the spacetime shear. This framework resolves ambiguities in defining Carrollian gravity and provides a robust theory for gravito-magnetic dynamics in ultra-relativistic regimes. Our results have direct implications for the study of black hole horizons, gravitational memory, and the holographic principle.

In curved spacetime, the dynamical equation of spinor fields is modified to account for Lorentz invariance violation (LIV). Based on the modified fermion dynamical equation, the quantum tunneling radiation properties of spin-1/2 fermions near the event horizon of higher-dimensional black holes are investigated. Focusing on the specific features of higher-dimensional Schwarzschild–de Sitter black hole and higher-dimensional Kerr–Anti–de Sitter black hole, this work explores the LIV-induced corrections to the Hawking temperature and the black hole entropy at the horizons of such black holes. New expressions are obtained for important black hole thermodynamic quantities, including the relation between the quantum tunneling rate and Hawking temperature, as well as the Bekenstein–Hawking entropy.

Abstract We obtain generally covariant operator-valued geodesic equations on a pseudo-Riemannian manifold M as part of the construction of quantum geodesics on the algebra $${\mathcal {D}}(M)$$ D ( M ) of differential operators. Geodesic motion arises here as an associativity condition for a certain form of first-order differential calculus on this algebra in the presence of curvature. The corresponding Schrödinger picture has wave functions on spacetime and proper time evolution by the Klein–Gordon operator, with stationary modes being solutions of the Klein–Gordon equation. As an application, we describe gravatom solutions of the Klein–Gordon equations around a Schwarzschild black hole, i.e. gravitationally bound states which far from the event horizon resemble atomic states with the black hole in the role of the nucleus. The spatial eigenfunctions exhibit probability density banding as for higher orbital modes of an ordinary atom, but of a fractal nature approaching the horizon.

Abstract We present the most general class of charged black hole solutions in third-order Lovelock gravity in even-dimensional spacetimes, incorporating an electromagnetic field and nonconstant-curvature horizons, which significantly influence the geometry for n ≥ 8. Unlike uncharged solutions, the near-origin behavior of the metric exhibits a timelike singularity for electrically charged black holes. Thermodynamic stability is analyzed in both the grand canonical and canonical ensembles. In the grand canonical ensemble, stability, determined by the positivity of both temperature and the Hessian determinant, imposes a lower bound on the event horizon radius below which black holes become unstable; this bound can vanish for specific electric, magnetic, or metric parameters, allowing stable configurations across all horizon sizes. In the canonical ensemble, stability is governed by the heat capacity, revealing both first-and second-order phase transitions. First-order transitions occur when the heat capacity vanishes or diverges at unphysical states, while second-order transitions take place between physical states and exhibit van der Waals-like behavior. Consequently, small and large black holes remain thermodynamically stable, whereas intermediate-sized configurations are unstable.

Abstract In this paper, we prove the codimension-one nonlinear asymptotic stability of the extremal Reissner–Nordström 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–Nordström 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–Nordström 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 nondecay and growth phenomena along the event horizon. Points (i) and (ii) above reflect the “stability” of the extremal Reissner–Nordström family and points (iii) and (iv) verify the presence of the celebrated Aretakis instability [11] for the linear wave equation on extremal Reissner–Nordström black holes in the full nonlinear Einstein–Maxwell-scalar field model.

Inflation with an inflection point potential is a popular model for producing primordial black holes. The potential near the inflection point is approximately flat, with a local maximum next to a local minimum, prone to eternal inflation. We show that a sufficient condition for eternal inflation is λ1 ≤ 3, where λ1 is the index of the 'exponential tail', the lowest eigenvalue of the Fokker-Planck equation over a bounded region. We write λ1 in terms of the model parameters for linear and quadratic regions. Wide quadratic regions inflate eternally if the second slow-roll parameter ηV ≥ -6. We test example models from the literature and show this condition is satisfied; we argue eternal inflation is difficult to avoid in inflection point PBH models. Eternally inflating regions correspond to type II perturbations and form baby universes, hidden behind black hole horizons. These baby universes are inhomogeneous on large scales and dominate the multiverse's total volume. We argue that, if volume weighting is used, eternal inflation makes inflection point primordial black hole models incompatible with large-scale structure observations.