Regular Black Hole Research Articles

Recovery of consistency in thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics

As one of candidate theories in the construction of regular black holes, Einstein's gravity coupled with nonlinear electrodynamics has been a topic of great concerns. Owing to the coupling between Einstein's gravity and nonlinear electromagnetic fields, we need to reconsider the first law of thermodynamics, which will lead to a new thermodynamic phase space. In such a phase space, the equation of state accurately describes the complete phase transition process of regular black holes. The Maxwell equal area law strictly holds when the phase transition occurs, and the entropy obeys the Bekenstein-Hawking area formula, which is compatible with the situation in Einstein's gravity.

Shadow and greybody bounding of a regular scale-dependent black hole solution

In this manuscript, we explore the shadow and the greybody bounding characteristics of a regular black hole within 4-dimensional space–time, employing the context of gravity that is scale-dependent. Our focus lies in determining limitations on the parameter denoted as ϵ̃, which serves as a descriptor for the scale-dependent solution with respect to the classically observed shadow radius Rsh as indicated in the documented data from the Event Horizon Telescope (EHT). Our result indicates that there is a unique value for ϵ̃ occurring at the reported mean of Rsh and the uncertainties could be the result of the fluctuating value of the scale-dependent parameter. We found that ϵ̃>0 is positive for Sgr. A*, but ϵ̃<0 for M87*. Utilizing M87* as a reference model, we scrutinized the shadow radius and weak deflection angle within the specified constraints. Discrepancies were observed not only in the shadow but also in the deflection angle of photons, particularly when the photon’s impact parameter closely approached the critical impact parameter.

Topological behavior of 3D regular black hole with zero point length

In this work, we study the thermodynamics and topological classes of regular black holes (RBH) in three dimensions, with charge, zero point length and rotational parameters in canonical, mixed and grand canonical ensembles. We consider the RBH in three dimensions with zero point length as defects with a topological nature within the thermodynamic domain and examine the local and global topology. We found that for non-rotating 3D RBH, the total topological number is 1 in the canonical ensemble whereas 0 in mixed and grand canonical ensembles While for rotating (rot) 3D RBH, the total topological number is 1 in the canonical ensemble, 0 in mixed ensemble, whereas −1 in grand canonical ensemble. We also found that for j=0, Q=0 the topological number is +1.

(Regular) Black holes in conformal Killing gravity coupled to nonlinear electrodynamics and scalar fields

In this work, we explore new solutions with static and spherical symmetry in 4D for black holes and regular black holes in the recently proposed conformal Killing gravity (CKG). This theory is of third order in the derivatives of the metric tensor and essentially satisfies three theoretical criteria for gravitational theories beyond general relativity (GR). The criteria essentially stipulate the following, that one should: (i) obtain the cosmological constant as an integration constant; (ii) derive the energy conservation law as a consequence of the field equations, rather than assuming it; (iii) and not necessarily consider conformally flat metrics as vacuum solutions. In fact, existing modified theories of gravity, including GR, do not simultaneously fulfil all of these three criteria. Here, we couple CKG to nonlinear electrodynamics (NLED) and scalar fields, and we explore solutions of black holes and regular black holes. More specifically, by solving the field equations of CKG, we find specific forms for the NLED Lagrangian, the scalar field and the field potential, and analyse the regularity of the solutions through the Kretschmann scalar. We find generalizations of the Schwarschild–Reissner-Nordström–AdS solutions, and consequently further extend the class of (regular) black hole solutions found in the literature.

Study of quasinormal modes, greybody factors, and thermodynamics within a regular MOG black hole surrounded by quintessence

In this article, we consider a regular black hole (BH) surrounded by quintessence in the scalar–vector–tensor (S–V–T) version of modified gravity (MOG). We examine the implications of the presence of a quintessence scalar field on astrophysical observable such as quasinormal modes (QNMs), greybody factors (GFs), and thermodynamics. In the vicinity of the MOG BH with quintessence, we calculate the effective potential generated by scalar and electromagnetic field perturbation, and then use the sixth order WKB method to compute the frequencies of the QNMs under these perturbations. We also study the impact of the MOG parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and the quintessence parameter c on QNM frequencies. Our investigation reveals that the combined effects of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and c parameters lead to significant decrease in oscillation frequencies, while the imaginary part generally rises. We then examine the GFs associated with the BH and found that as the model parameters α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and c increase, GF also increases, and thus less scattering. Additionally, we investigate the thermodynamic quantities and geometries for asymptotically expanded MOG BH. Through heat capacities, Helmholtz and Gibbs free energies, it is observed that this BH shows the stable behavior for various choices of the state parameter of the quintessence ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}. It is also interesting to mentioned here that Weinhold geometry exhibits the repulsive nature and Ruppiener geometry provides the attractive nature of MOG on the particles for most of the choices of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}.

Gravitational repulsive effects in 3D regular black holes

Gravitational repulsive effects in 3D regular black holes

Implications of a Simpson–Visser solution in Verlinde’s framework

This study focuses on investigating a regular black hole within the framework of Verlinde’s emergent gravity. In particular, we explore the main aspects of the modified Simpson–Visser solution. Our analysis reveals the presence of a unique physical event horizon under certain conditions. Moreover, we study the thermodynamic properties, including the Hawking temperature, the entropy, and the heat capacity. Based on these quantities, our results indicate several phase transitions. Geodesic trajectories for photon-like particles, encompassing photon spheres and the formation of black hole shadows, are also calculated to comprehend the behavior of light in the vicinity of the black hole. Additionally, we also provide the calculation of the time delay and the deflection angle. Corroborating our results, we include an additional application in the context of high-energy astrophysical phenomena: neutrino energy deposition. Finally, we investigate the quasinormal modes using third-order WKB approximation.

Dust Collapse in Asymptotic Safety: A Path to Regular Black Holes.

Regular black hole spacetimes are obtained from an effective Lagrangian for quantum Einstein gravity. The interior matter is modeled as a dust fluid, which interacts with the geometry through a multiplicative coupling function denoted as χ. The specific functional form of χ is deduced from asymptotically safe gravity, under the key assumption that the Reuter fixed point remains minimally affected by the presence of matter. As a consequence the gravitational coupling vanishes at high energies. The static exterior geometry of the black hole is entirely determined by the junction conditions at the boundary surface. Consequently, the resulting global spacetime geometry remains devoid of singularities at all times. This outcome offers a new perspective on how regular black holes are formed through gravitational collapse.

Quasinormal modes and isospectrality of Bardeen (Anti-) de Sitter black holes* *Supported by the the Natural Science Foundation of Hunan Province, China (2022JJ40262), and the National Natural Science Foundation of China (12375046, 12205254)

Black holes (BHs) exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes (RBHs). The initial formulation of RBHs was presented by Bardeen, who considered the Einstein equation coupled with a nonlinear electromagnetic field. In this study, we investigate the gravitational perturbations, including the axial and polar sectors, of the Bardeen (Anti-) de Sitter black holes. We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes (QNMs) through numerical methods. For the Bardeen de Sitter black hole, we employ the 6th-order WKB approach. The numerical results reveal that the isospectrality is broken in this case. Conversely, the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.

Exploring thin-shell dynamics in regular charged black hole through T-duality

We present a thin-shell in the background of a regular charged static black hole solution in the presence of T-duality effects for the Einstein–Maxwell system. The thin-shell are developed by matching the inner and outer manifolds through the well-known Visser’s cut-and-paste approach. We produce three types of thin-shells with an outer regular charged black hole from T-duality and different choices of inner manifolds named: 1. Thin-shell (inner flat spacetime), 2. Thin-shell Garvastars (inner de Sitter spacetime), and 3. Thin-shell wormholes (inner regular charged black hole from T-duality) We evaluate the surface stresses of a thin layer of matter contents at a thin-shell through Lanczos equations and also develop equations of motion of these constructed configurations. We also explore thin-shell stability through linearized radial perturbations at equilibrium shell radius with barotropic and generalized Chaplygin equations of state. We show that the stability of respective configurations enhances in the presence of exterior charged BH from T-duality. We conclude that thin-shell Garvastars are more stable than thin-shell and thin-shell wormholes.

From regular black holes to horizonless objects: quasi-normal modes, instabilities and spectroscopy

We study gravitational and test-field perturbations for the two possible families of spherically symmetric black-hole mimickers that smoothly interpolate between regular black holes and horizonless compact objects accordingly to the value of a regularization parameter.One family can be described by the Bardeen-like metrics, and the other by the Simpson-Visser metric.We compute the spectrum of quasi-normal modes (QNMs) of these spacetimes enlightening a common misunderstanding regarding this computation present in the recent literature.In both families, we observe long-living modes for values of the regularization parameter corresponding to ultracompact, horizonless configurations. Such modes appear to be associated with the presence of a stable photon sphere and are indicative of potential non-linear instabilities.In general, the QNM spectra of both families display deviations from the standard spectrum of GR singular BHs.In order to address the future detectability of such deviations in the gravitational-wave ringdown signal, we perform a preliminary study, finding that third generation ground-based detectors might be sensible to macroscopic values of the regularization parameter.

Radiative characteristics of accretion disksaround rotating regular black holes

Radiative characteristics of accretion disksaround rotating regular black holes

Regular black hole from a confined spin connection in Poincaré gauge gravity

Within the asymptotic safety program, it is possible to construct renormalization group (RG) improved spacetimes by replacing the gravitational coupling G by its running counterpart G(k), and subsequently identifying the RG scale k with a physical distance scale. This procedure has been used to construct a regular Schwarzschild geometry, but it fails in the presence of a cosmological constant. This can only be avoided if the dimensionless cosmological constant has a trivial ultraviolet fixed point, but so far no such scenario has been encountered in quantum general relativity (with or without matter). In this Letter we provide a possible solution to this problem. In Poincaré gauge gravity an effective cosmological constant arises naturally, and if the non-Abelian Lorentz spin connection is asymptotically free, it generates a trivial ultraviolet fixed point for this cosmological constant. We thereby tentatively propose a nonsingular black hole consistent with the principles of asymptotic safety, embedded in Poincaré gauge gravity.

Stress-energy tensor correlations across regular black holes horizons

Stress-energy tensor correlations across regular black holes horizons

Kinematic and energy properties of dynamical regular black holes

Kinematic and energy properties of dynamical regular black holes

Accretion disk for regular black holes with sub-Planckian curvature

Accretion disk for regular black holes with sub-Planckian curvature

Analysis of a regular black hole in Verlinde’s gravity

This work focuses on the examination of a regular black hole within Verlinde’s emergent gravity, specifically investigating the Hayward-like (modified) solution. The study reveals the existence of three horizons under certain conditions, i.e. an event horizon and two Cauchy horizons. Our results indicate regions which phase transitions occur based on the analysis of heat capacity and Hawking temperature. To compute the latter quantity, we utilize three distinct methods: the surface gravity approach, Hawking radiation, and the application of the first law of thermodynamics. In the case of the latter approach, it is imperative to introduce a correction to ensure the preservation of the Bekenstein–Hawking area law. Geodesic trajectories and critical orbits (photon spheres) are calculated, highlighting the presence of three light rings. Additionally, we investigate the black hole shadows. Furthermore, the quasinormal modes are explored using third- and sixth-order Wentzel–Kramers–Brillouin approximations. In particular, we observe stable and unstable oscillations for certain frequencies. Finally, in order to comprehend the phenomena of time-dependent scattering in this scenario, we provide an investigation of the time-domain solution.

GEMS Embeddings of Hayward Regular Black Holes in Massless and Massive Gravities

After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass holographically by broken momentum conservation in the HRBH. The original HRBH has no holographically added gravitons, which we call ‘massless’. Making use of newly found embedding coordinates, we obtain desired Unruh temperatures and compare them with the Hawking and local fiducial temperatures, showing that the Unruh effect for a uniformly accelerated observer in a higher-dimensional flat spacetime is equal to the Hawking effect for a fiducial observer in a black hole spacetime. We also obtain freely falling temperatures of the HRBHs in massless and massive gravities seen by freely falling observers, which remain finite even at the event horizons while becoming the Hawking temperatures in asymptotic infinity.

Unveiling the unconventional optical signatures of regular black holes within accretion disk

The optical characteristics of three types of black holes (BHs) surrounded by a thin accretion disk are discussed, namely the Schwarzschild BH, Bardeen BH, and Hayward BH. We calculate the deflection angle of light as it traverses the vicinity of each BH using numerical integration and semi-analytical methods, revealing that both approaches can effectively elucidate the deflection of light around the BH. We investigate the optical appearance of the accretion disk and its corresponding observational images at various viewing angles, discovering that the luminosity in the region near the BH on the inner side of the accretion disk is higher than that on the outer side owing to higher material density in closer proximity to the BH. We observe a significant accumulation of brightness on the left side of the accretion disk, attributed to the motion of matter and geometric effects. Our findings emphasize the significant influence of the observation inclination angle on the observed outcomes. An increase in the observation inclination angle results in the separation of higher-order images. With the improvement in EHT observation accuracy, we believe that the feature of a minimal distance between the innermost region of the direct image of the Hayward BH and the outermost region of the secondary image can be used as an indicator for identifying Hayward BHs.

A regular black hole as the final state of evolution of a singular black hole

We propose a novel black hole model in which singular and regular black holes are combined as a whole and more precisely singular and regular black holes are regarded as different states of parameter evolution. We refer to them as singular and regular states, respectively. Furthermore, the regular state is depicted by the final state of parameter evolution in the model. We also present the sources that can generate such a black hole spacetime in the framework of F(R) gravity. This theory of modified gravity is adopted because it offers a possible resolution to a tough issue in the thermodynamics of regular black holes, namely the discrepancy between the thermal entropy and Wald entropy. The dynamics and thermodynamics of the novel black hole model are also discussed when a singular state evolves into a regular state during the change of charge or horizon radius from its initial value to its extreme value.