Search Results (183)

We investigate null geodesics, photon spheres and black hole shadows for the static spherically symmetric non-Schwarzschild black hole solution of Einstein–Weyl gravity, a higher-derivative extension of General Relativity containing a quadratic Weyl-curvature term. Such higher-curvature theories are motivated by attempts to formulate a quantum theory of gravity, where they improve the ultraviolet behaviour of the gravitational interaction, and also arise naturally as effective descriptions in approaches such as string theory. We employ the numerical black hole solution obtained by Lü et al. to compute the photon sphere, the shadow radius and the angular size of the shadow as observed by static observers. We show that, for black holes of equal mass, the photon sphere, shadow radius and angular size are consistently larger than those of the corresponding Schwarzschild black hole, with the deviations increasing monotonically with the higher-curvature coupling parameter $\alpha$. Motivated by the Event Horizon Telescope observations of M87* and Sagittarius A*, we further compare the predicted shadow size with current observational uncertainties and derive phenomenological upper bounds on the dimensionless coupling $\alpha /m^2$. These results demonstrate that black hole shadow observations provide a promising avenue for testing Einstein–Weyl gravity and constraining quantum-motivated higher-curvature corrections to General Relativity. Full article

This work aims to explore the gravitational consequences of a recently proposed black hole solution previously introduced, which incorporates quantum gravitational corrections of General Relativity. We initiate our analyses by taking into account the horizon structure, focusing on both the event and Cauchy horizons. Subsequently, we examine the quasinormal modes by considering all types of perturbations—scalar, vector, tensor, and spinorial. To strengthen these results, we also compute the time domain for each perturbation. Next, we turn to the study of optical properties of the black hole. In particular, we investigate null geodesics, the photon sphere and its stability, and the corresponding black hole shadows. Following this, we analyze gravitational lensing phenomena in two regimes: the weak-field limit, utilizing the Gauss–Bonnet theorem, and the strong deflection limit, employing Tsukamoto’s approach. In addition, we address the lensing observables with Event Horizon Telescope (EHT) data for $SgrA*$ and $M87*$. Finally, constraints on the parameter $\xi$—which is introduced by higher-order curvature–scalar gravity, thereby differing from the Schwarzschild solution—are estimated using Solar System measurements such as the precession of Mercury’s orbit, gravitational light bending, and time delay (or the Shapiro effect). Full article

We study gravitational lensing by $k-n$ generalized black-bounce space-times both in regimes of weak and strong field approximations. These metrics interpolate between regular black holes and one-way or traversable wormholes. First, we investigate the light-like geodesic trajectories and derive an analytical expression for the deflection angle in terms of the bounce parameter in the weak-field gravitational regime. We then turn to the strong-field gravitational regime and display the behavior of the bending angle as a function of both the impact parameter and the bounce parameter. Next, using the lens equations, we analyze how the observables for Sagittarius A* behave concerning the bounce parameter. We obtain the shadow’s radii for some black-bounce metrics and plot the graph of their sizes, comparing them with the Schwarzschild one. Full article

Recent theoretical studies propose that Hawking radiation may not emerge strictly at the event horizon but rather from the spatially extended region surrounding a black hole, commonly referred to as the quantum atmosphere. In this work, we explore how this concept influences nonlocal quantum correlations in a bosonic bipartite system located at a certain distance from a Schwarzschild black hole. By employing the measurement-induced nonlocality (MIN) as a quantifier of quantum correlations, we analyze the response of bosonic fields to the thermal and geometric characteristics associated with the Hartle–Hawking vacuum. Those features are associated with the coordinate-dependent metric components of the Schwarzschild background. In this manner, we extend previous studies that primarily focused on the fermionic systems. Our results reveal that when the quantum atmosphere is taken into account, the behavior of MIN departs from its conventional near-horizon profile. In particular, bosonic nonlocal correlations are found to exhibit a pronounced degradation at a finite radial distance from the event horizon and to ultimately vanish as the scaled distance increases further. To some extent this behavior contrasts with the previously considered fermionic case, indicating that bosonic fields provide a potentially stronger response to the quantum atmosphere. Full article

This paper investigates scaling symmetry in thermodynamics by unifying constrained Hamiltonian dynamics with symplectic and contact geometries. Through the mathematical processes of contactization and symplectization, we demonstrate that fixing an extended global scale variable effectively recovers the standard thermodynamic description in terms of scale-invariant quantities. The geometric formalism is illustrated by establishing the diffeomorphism between the Lagrangian submanifolds of ideal and van der Waals gases. Finally, applying this framework to a Schwarzschild black hole reveals that changing the scaling weights of entropy and internal energy is a fundamental physical requirement to accommodate non-isothermal dynamics. Full article

We present a path-based curvature representation of the gravitational bending of light in black-hole (BH) spacetimes. The bending angle is written as a one-dimensional line integral of the optical Gaussian curvature ${\mathcal{K}}_{\mathrm{opt}}$ along the photon trajectory, weighted by a geometric kernel $W(r,b)$. This representation sits within the Gibbons–Werner Gauss–Bonnet (GB) optical-geometry family rather than alongside it: the kernel is fixed by a co-area reduction of the GB surface integral along an undeflected reference path, and the single new computational object is the resulting radial integral together with its cumulative, directly plottable reading of how the deflection builds up along the ray. With the lever-arm choice $W=\sqrt{r^2-b^2}$, the integral reproduces $\hat{\alpha }=4M/b$ for every static, asymptotically flat metric (Theorem 1) and evaluates in closed form for Schwarzschild, Reissner–Nordström (RN), and equatorial Kerr. The representation becomes reliable at a large impact parameter; at the small impact parameters relevant to horizon-scale imaging, it is not numerically competitive with the standard expansions, a limitation we quantify. Beyond leading order the kernel must import information from the bent geodesic, after which the scheme reconstructs the known perturbative series; the second-order mismatch in the lever-arm result therefore measures, rather than hides, the deformation of the photon path away from the straight-line reference. Finite source–observer distances enter through the Ono–Ishihara–Asada (OIA) construction, and a winding-sum continuation outlines the route toward the strong-deflection regime, whose closed-form reduction is left to future work. Full article

Regular black-hole models replace the Schwarzschild singularity with a finite inner core, thereby removing the geometric endpoint at which the classical spacetime description breaks down. This issue is relevant to black-hole quantum information, since a singular interior prevents a regular effective description of interior degrees of freedom and horizon correlations. In this work, the regular black-hole geometry introduced by Dymnikova is used as a compact, single-scale effective background for black-hole quantum information considerations. The aim is not to propose a new regular metric but to clarify how an established finite-core geometry can support a nonsingular description of the Schwarzschild interior at the effective level. The geometry preserves the Schwarzschild asymptotic limit while replacing the divergent central region with a finite de Sitter-like core. The curvature invariants remain finite, and the effective source admits an anisotropic-fluid interpretation whose central limit is isotropic and vacuum-like. This use therefore provides a minimal geometric setting, rather than a newly proposed metric solution, for discussing nonsingular black-hole interiors. It does not establish unitary evaporation, information recovery, dynamical stability, or a microscopic quantum-gravity mechanism. Instead, it identifies a finite-curvature spacetime framework in which questions concerning interior quantum degrees of freedom and horizon entanglement can be formulated without encountering a curvature singularity. Full article

We investigate a static and spherically symmetric Schwarzschild–Letelier Black Hole immersed in a King Dark Matter Halo and analyze how the combined effects of the cloud of strings and the dark-matter environment modify the spacetime geometry, particle dynamics, and thermodynamic behavior of the black hole. Particular attention is devoted to the motion of both massless photons and massive test particles in this black hole background. In the geodesic analysis, we derive the effective potential and study the properties of circular photon orbits, the associated black-hole shadow radius, and the innermost stable circular orbit (ISCO), highlighting the role played by the cloud of strings parameter and the King dark-matter halo parameters in shifting the orbital structure relative to the standard Schwarzschild case. To further characterize the spacetime from a topological perspective, we investigate the unstable circular null orbit using a normalized vector field constructed within the framework of Duan’s $\varphi$-Mapping Topological Current Theory. Through this method, we identify the corresponding topological charge and examine the relation between the photon sphere and the underlying topological structure of the black-hole configuration. In addition, we explore the thermodynamic properties of the system by computing the Hawking temperature, entropy, Helmholtz free energy, and heat capacity, thereby analyzing the black hole’s local and global thermodynamic stability. The influence of the surrounding dark-matter halo and cloud of strings on the phase structure and thermal behavior is discussed in detail. We further study the thermodynamic topology of the system via the off-shell free-energy formalism, which provides insight into possible thermodynamic phase transitions and the topological classification of black-hole states. Our analysis demonstrates that the combined effects of the cloud of strings and the King dark-matter halo significantly modify the horizon structure, geodesic dynamics, shadow characteristics, and thermodynamic properties of the black hole when compared with the standard Schwarzschild solution. Full article

The entropy of a Schwarzschild black hole is commonly derived using thermodynamic relations whose physical interpretation is not always transparent, in particular with respect to the localization of temperature and entropy. In this paper, we present a derivation of the Bekenstein–Hawking entropy based exclusively on the principles of phenomenological thermodynamics, formulated entirely in regions where spacetime is effectively flat. The analysis considers a reversible evaporation process in which the black hole is surrounded by a tunable thermal radiation bath whose temperature is kept arbitrarily close to the Hawking temperature. In this limit, entropy production can be made negligible. By integrating the entropy flux through a distant reference surface over the evaporation process, the standard entropy formula is obtained without invoking assumptions about the localization of the black hole entropy or about microscopic degrees of freedom. The derivation is mathematically simple but conceptually instructive. The approach is intended to be accessible to readers familiar with classical thermodynamics and general relativity at an advanced undergraduate or graduate level. Full article

We develop a general framework for quantum field theory in curved spacetime based on Local Minkowski Coordinates (LMC), which incorporates curvature effects into local Feynman diagrammatics. Gravitational influence enters through a curvature-dependent normalization function $B\left(x\right)$, derived from covariant current conservation, and a gravitational phase $S\left(x\right)$, obtained via the WKB approximation. These quantities enter through local phase accumulation and observer-dependent normalization of external states, without modifying globally conserved fluxes. As a first application, we analyze the local redshift normalization and phase structure of quantum amplitudes in the vicinity of a Schwarzschild black hole. Within their range of validity, the curvature-dependent factors $B\left(x\right)$ and $S\left(x\right)$ reproduce the expected gravitational redshift of field amplitudes in general relativity. When amplitudes are propagated to asymptotic infinity and evaluated in a standard global quantum state (such as the Unruh state), the resulting flux is consistent with the standard Hawking result. The framework refines the local WKB structure and clarifies the separation between local normalization effects and globally conserved fluxes. Full article

While the standard Schwarzschild metric is overwhelmingly employed in general relativity (GR) as the starting point for various spherical spacetime metric calculations, its isotropic (ISO) form is mentioned in more specialized contexts and its derivation is barely discussed in published GR literature. In this work, we review the isotropic metric, stressing that it stands out as a useful spherically symmetric metric to be employed also in traditional GR problems. We start by deriving the ISO metric through solving the vacuum field equations in Cartesian coordinates, thereby obtaining the Ricci tensor also in spherical coordinates. We then analytically calculate the Riemann tensor in Cartesian coordinates, proving its consistency with the Ricci tensor calculation for pedagogical reasons. Finally, from the Riemann tensor we exactly evaluate the Kretschmann scalar, which lacks metric singularities, a result consistent with the known singular behavior of the standard Schwarzschild metric. We conclude that the isotropic metric naturally emerges as a suitable candidate for modeling static neutron stars and regular black holes, thereby complementing the present attempts to understand these rapidly evolving research fields. Full article

The derivations presented in this paper suggest an intimate relationship between geometry and the electroweak sector at the Planck scale. A Lorentz-invariant maximally symmetric stochastically perturbed spacetime transformed to spherical coordinates reveals an emergent Schwarzschild metric, entirely a statistical structure of stochastic spacetime. Similarly, the transition from a maximally symmetric universe with a complex $SU\left(2\right)$ scalar doublet $\varphi$, comprising four independent real scalar fields with a zero vacuum expectation value (VEV), to spherical coordinates at the Planck scale reveals the spontaneously broken electroweak (EW) sector. Working in the unitarity gauge, the resulting EW potential can be simultaneously mapped in space at the Planck scale and across the EW sector. In space, the resulting EW potential includes a deep well within the Schwarzschild sphere and a shallow well just outside corresponding to an accretion disk. The same potential mapped in the EW space provides an entire family of possible sombrero hat potentials with fourth-order coupling specific to a point in space. At the minimum points of the potential in space, inside the Schwarzschild sphere and at the accretion disk, the $\lambda$ corresponding to the Standard Model (SM) fourth-order coupling is instead derived as $\frac{\lambda }{5}$. The factor of $\frac{1}{5}$ is a simple consequence of the conservation of the EW VEV and the fact that the SM formulation of the EW potential does not account for situations where the perturbations in $\varphi$ dominate. A more general formulation of the EW potential restores the SM quartic coupling and preserves $\lambda$ in space. An emergent Higgs field inside the Schwarzschild black hole is found to directly relate to the stochastic spacetime fields normalized by the Schwarzschild radius. The corresponding Higgs vacuum has both a ground and excited state and the possibility of both positive and negative vacuum entropy. Finally, the scalar-field VEV degeneracy in EW space of the metastable Higgs vacuum appears instead differentiated in space with possible probability, tunneling, and entropy implications. Full article

In this work, we propose a modified Schwarzschild geometry inspired by the Asymptotic Safety approach to quantum gravity, in which the Newtonian coupling becomes a running quantity depending on the radial coordinate. We employ an infrared cutoff at the proper distance and obtain a new quantum-corrected black hole metric. We provide a thermodynamical analysis, first using standard methods and then proceeding to a geometrothermodynamical study of the phase space and to a topological analysis of phase transitions. We also calculate the grey-body factors of our solution, providing exact lower bounds in the quantum-corrected transmission coefficients. Finally, we present the shadow size and intensity profile of our solution, showing its consistency with current observational constraints. Full article

We quantize the exterior region of a Schwarzschild–AdS black hole using our model of quantum gravity. The resulting hyperbolic equation is solved by products of temporal eigenfunctions $w_i$, the eigenvalues of which all have multiplicity one, and spatial eigendistributions $v_{ij}$ having the same eigenvalues but with multiplicities $1\le m_i$, where the $m_i$ could in principle be arbitrarily large. Regarding only the exterior region, there was no guidance how to determine the values of the $m_i$. However, considering also the quantization of the interior region, where the same question did not arise since the $m_i$ could be chosen by maximizing the value, it seemed logical to choose the same values, too, in the exterior case. Since the eigenvalues in the interior are the same because the temporal Hamiltonian is the same in both cases, this choice defined a unitary equivalence between the respective Hilbert spaces and the respective Hamiltonians. Hence, there is no information paradox on a quantum level. Full article

Here we investigate a possible presence of a fifth force at the Galactic Center (GC), and its potential influence on the stellar orbits around the central supermassive black hole (SMBH) of our Galaxy. For this purpose we simulated the stellar orbits in a Yukawa gravity model that predicts the emergence of a fifth force, and fitted them into the observed orbit of S2 star around Sgr A* at the GC. The fitting was performed using Markov chain Monte Carlo (MCMC) method which enabled us to constrain the parameters of Yukawa interaction describing the strength $\delta$ and the range $\lambda$ of a fifth force. We studied the following cases for a fifth force range $\lambda$: (i) when it is about a few hundred AU (i.e., deep inside the orbit of S2 star), (ii) when it is about a thousand AU (i.e., approximately the size of S2 star orbit), and (iii) when it is several thousand AU (i.e., much larger than the size of S2 star orbit). The obtained results showed that as the range $\lambda$ of a fifth force increases, its strength $\delta$ also increases and relative error $\Delta \delta /\delta$ decreases. The resulting fifth-force strengths in all three cases are respectively: $\delta$∼0.005, 0.02 and 0.15. These results are consistent with the corresponding results of both our previous studies and those of other authors, regardless of the different Yukawa-like potentials used to model a fifth force. In addition, assuming that the orbital precession of S2 star is close to the prediction of General Relativity (GR) for its Schwarzschild precession, we studied whether the possible small discrepancies from this prediction could be also caused by a fifth force. For this purpose we used the $f_{\mathrm{SP}}$ parameter that was recently measured in the case of S2 star by GRAVITY Collaboration in 2020, and that describes the extent to which some gravitational model is relativistic. We found that the obtained estimates in all three cases are compatible, within the error intervals, with the measured value of $f_{\mathrm{SP}}=1.10\pm 0.19$. Full article