Narrow Results

Recently, there has been an interest in exploring black holes that are regular in the sense that the central curvature singularity is avoided. Here, we depict a method to obtain a regular black hole (RBH) spacetime from the unhindered gravitational collapse beginning with regular initial data of a spherically symmetric perfect fluid. In other words, we obtain the equilibrium (static) spacetime $(\mathcal{ℳ},\tilde{g})$ as a limiting case of the time-evolving (nonstationary) spacetime $(\mathcal{ℳ},g)$. In the spirit of P. S. Joshi, D. Malafarina and R. Narayan, Class. Quantum Grav. 31 (2014) 015002, our description of gravitational collapse is implicit in nature in the sense that we do not describe the data at each time-slice. Rather, we impose a condition in terms of geometric and matter variables for the collapse to have an end-state that is devoid of incomplete geodesics but admits a marginally trapped surface (MTS). The admission of MTS causally disconnects two mutually exclusive regions ${\widehat{\mathcal{ℳ}}}_1$ and ${\widehat{\mathcal{ℳ}}}_2\subset \mathcal{ℳ}$ in the sense that $\forall p\in {\widehat{\mathcal{ℳ}}}_2$, the causal past of p does not intersect ${\widehat{\mathcal{ℳ}}}_1$. While the classic Oppenheimer–Snyder collapse model necessarily produces a black hole with a Schwarzschild singularity at the center, we show here that there are classes of regular initial conditions for which the collapse gives rise to a RBH.

Regular black holes are crucially important as approaches to solving the singularity problem, and in this paper, the accretion disk of Bardeen and Hayward models has been studied. For this purpose, we calculated the physical properties of black holes, including radiant energy, luminosity derivative, temperature, and conversion efficiency of accretion mass into radiation. The obtained results show that the nonzero-free parameters of regular black holes cause the radius of the innermost stable circular orbit of the disk to shift to smaller values. As a result of this displacement, we saw an increase in the profiles of radiant energy, luminosity derivative, and temperature. We also find that Bardeen and Hayward’s black holes are more efficient in converting mass to radiation than Schwarzschild. Finally, we compared the free parameter of these two black holes with the spin of the rotating black hole and found that the Bardeen and Hayward black holes can mimic the slowly rotating Kerr black hole.

It is shown that the near-horizon geometry of a generic extreme regular black hole solution of Einstein gravity coupled to nonlinear electrodynamics is described by the AdS₂ × S² spacetime.

We study the four-dimensional (i) modified Bardeen black hole, (ii) modified Hayward black hole, (iii) charged regular black hole and (iv) magnetically charged regular black hole. For modified Bardeen black hole and modified Hayward black hole, we found only one horizon (event horizon) and then we found some thermodynamic quantities like the entropy, surface area, irreducible mass, temperature, Komar energy and specific heat capacity on the event horizon. We here study the bounds of the above thermodynamic quantities for these black holes on the event horizon. Then, we examine the thermodynamics stability of the black holes with some conditions. Next, we studied the charged regular black hole and magnetically charged regular black hole and found two horizons (Cauchy and event horizons) of these black holes. Then, we found the entropy, surface area, irreducible mass, temperature, Komar energy and specific heat capacity on the Cauchy and event horizons. Then, we get some conditions for thermodynamic stability/instability of the black holes. We found the radius of the extremal horizon and Christodoulou–Ruffiini mass and then analyze the above thermodynamic quantities on the extremal horizon. We calculate the sum/subtraction, product, division and sum/subtraction of inverse of surface areas, entropies, irreducible masses, temperatures, Komar energies and specific heat capacities on both the horizons. From these, we found the bounds of the above quantities on the horizons.

In this work, we join the controversial discussion on singular and nonsingular black holes using the Gaussian distribution. Our result which uses correct boundary conditions shifts the debate in favor of regular black holes at the center. The present findings add new insights into the ongoing discussions surrounding singularities in black hole solutions of the Einstein equations.

We consider self-consistent coupling of bulk Einstein–Maxwell–Kalb–Ramond system to codimension-one charged lightlikep-brane with dynamical (variable) tension (LL-brane). The latter is described by a manifestly reparametrization-invariant worldvolume action significantly different from the ordinary Nambu–Goto one. We show that the LL-brane is the appropriate gravitational and charge source in the Einstein–Maxwell–Kalb–Ramond equations of motion needed to generate a self-consistent solution describing nonsingular black hole. The latter consists of de Sitter interior region and exterior Reissner–Nordström region glued together along their common horizon (it is the inner horizon from the Reissner–Nordström side). The matching horizon is automatically occupied by the LL-brane as a result of its worldvolume Lagrangian dynamics, which dynamically generates the cosmological constant in the interior region and uniquely determines the mass and charge parameters of the exterior region. Using similar techniques we construct a self-consistent wormhole solution of Einstein–Maxwell system coupled to electrically neutral LL-brane, which describes two identical copies of a nonsingular black hole region being the exterior Reissner–Nordström region above the inner horizon, glued together along their common horizon (the inner Reissner–Nordström one) occupied by the LL-brane. The corresponding mass and charge parameters of the two black hole "universes" are explicitly determined by the dynamical LL-brane tension. This also provides an explicit example of Misner–Wheeler "charge without charge" phenomenon. Finally, this wormhole solution connecting two nonsingular black holes can be transformed into a special case of Kantowski–Sachs bouncing cosmology solution if instead of Reissner–Nordström we glue together two copies of the exterior Reissner–Nordström–de Sitter region with big enough bare cosmological constant, such that the radial coordinate becomes a timelike variable everywhere in the two "universes," except at the matching hypersurface occupied by the LL-brane.

We discuss the problem of identification of coupling constants, which describe interactions between photons and spacetime curvature, using exact regular solutions to the extended equations of the nonminimal Einstein–Maxwell theory. We argue the idea that three nonminimal coupling constants in this theory can be reduced to the single guiding parameter, which plays the role of nonminimal radius. We base our consideration on two examples of exact solutions obtained earlier in our works: the first of them describes a nonminimal spherically symmetric object (star or black hole) with regular radial electric field; the second example represents a nonminimal Dirac-type object (monopole or black hole) with regular metric. We demonstrate that one of the inflexion points of the regular metric function identifies a specific nonminimal radius, thus marking the domain of dominance of nonminimal interactions.

We discuss the phenomenology of massless scalar fields around a regular Bardeen black hole, namely absorption cross-section, scattering cross-section and quasinormal modes. We compare the Bardeen and Reissner–Nordström black holes, showing limiting cases for which their properties are similar.

So far the study of black hole perturbations has been mostly focused upon the classical black holes with singularities at the origin and hidden by event horizon. Compared to that, the regular black holes are a completely new class of solutions arising out of modification of general theory of relativity by coupling gravity to an external form of matter. Therefore it is extremely important to study the behavior of such regular black holes under different types of perturbations. Recently a new regular Bardeen black hole solution with a de Sitter branch has been proposed by Fernando [arXiv:1611.05337 [gr-qc]]. We compute the quasi-normal (QN) frequencies for the regular Bardeen de Sitter (BdS) black hole due to massless and massive scalar field perturbations as well as the massless Dirac perturbations. We analyze the behavior of both real and imaginary parts of QN frequencies by varying different parameters of the theory.

We present a review on Lagrangian models admitting spherically symmetric regular black holes (RBHs), and cosmological bounce solutions. Nonlinear electrodynamics, nonpolynomial gravity, and fluid approaches are explained in details. They consist respectively in a gauge invariant generalization of the Maxwell–Lagrangian, in modifications of the Einstein–Hilbert action via nonpolynomial curvature invariants, and finally in the reconstruction of density profiles able to cure the central singularity of black holes. The nonpolynomial gravity curvature invariants have the special property to be second-order and polynomial in the metric field, in spherically symmetric spacetimes. Along the way, other models and results are discussed, and some general properties that RBHs should satisfy are mentioned. A covariant Sakharov criterion for the absence of singularities in dynamical spherically symmetric spacetimes is also proposed and checked for some examples of such regular metric fields.

The main objective of this work is the construction of regular black hole solutions in the context of the Einstein–Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this purpose, we first write explicitly the Einstein field equations for the interior regular region. We take an electrically charged nonisotropic fluid, which presents spherical symmetry and a de Sitter type equation of state, where the radial pressure $p_r$ is equal to the negative of energy density $\rho$, $p_r=-\rho$. Then, two solutions for the Einstein equations are built, a regular interior solution for the region with matter satisfying a de Sitter equation of state, and an external solution for the region outside the matter, that corresponds to the Reissner–Nordström metric. To complete the solution we apply the Darmois–Israel junction conditions with a timelike thin shell at the matching surface. It is assumed that the matching surface is composed by a thin shell of matter, i.e. a surface layer in the form of a perfect fluid obeying a barotropic equation of state, ${𝒫}=\omega \sigma ,P$ and $\sigma$ being the intrinsic pressure and energy density of the shell, respectively, and $\omega$ a constant parameter. We show that there are electrically charged regular black hole solutions and other compact objects for specific choices of $\omega$ and of the other parameters of the model. Some properties the objects are investigated.

Bardeen regular black hole is commonly considered as a solution of general relativity coupled to a nonlinear electrodynamics. In this paper, it is shown that the Bardeen solution may be interpreted as a quantum-corrected Schwarzschild black hole. This new interpretation is obtained by means of a generalized uncertainty principle applied to the Hawking temperature. Moreover, using the regular black hole of Bardeen, it is possible to evaluate the quantum gravity parameter of the generalized uncertainty principle or, assuming the recent upper bounds for such a parameter, to verify an enormous discrepancy between a cosmological constant and that measured by recent cosmological observations $(\sim 10^{120})$.

Tidal forces produced by black holes are an important result of General Relativity related to the spacetime curvature tensor. Among the astrophysical implications of tidal forces, the tidal disruption events stand out. We analyze the tidal forces in the spacetime of an electrically charged Hayward regular black hole, obtaining the components of the tidal tensor and the geodesic deviation equation. We find that the radial and angular tidal forces may vanish and change sign unlike in the Schwarzschild spacetime. We note that tidal forces are finite at the origin of the radial coordinate in this regular black hole spacetime. We obtain the geodesic deviation vector for a body constituted of dust infalling towards the black hole with two different initial conditions.

A regular static, spherically symmetric electrically charged black hole solution of general relativity coupled to a new theory for nonlinear electrodynamics is presented. This theory has the interesting feature that, at far distances from the black hole, in the weak field limit, the theory reduces to Maxwell Lagrangian with Heisenberg–Euler correction term of quantum electrodynamics. The singular center of the black hole is replaced by flat, de Sitter, or anti de Sitter space, if the spacetime in which the black hole is embedded is asymptotically flat, de Sitter, or anti de Sitter, respectively. Requiring the correspondence to Heisenberg–Euler Lagrangian at large distances, in the weak field limit, we find that (i) a minimum mass is required for the formation of an event horizon for the regular static, spherically symmetric solution of the theory, and, (ii) the mass of the solution must be quantized. We also study the basic thermodynamic properties of the black hole solution and show that they are qualitatively similar to those of Reissner–Nordström black hole.

In this paper, we explore the dynamics of test particles in spacetime around regular Bardeen black holes (BHs) in the novel four-dimensional Einstein–Gauss–Bonnet (4D EGB) theory. First, we analyze properties of the spacetime around the Bardeen BH with respect to the Gauss–Bonnet (GB) coupling parameter $\alpha$, and we show the range of values of the BH charge and the parameter $\alpha$ that horizon exists as $\alpha /M^2\in (-0.15869,1)$ and $g/M\in (0,0.886247)$, respectively. We also investigate the effects of the magnetic charge of the regular BH on innermost stable circular orbits (ISCOs) radius and efficiency of energy release from infalling test particles to the regular Bardeen BH in 4D EGB gravity. Moreover, fundamental frequencies such as Keplerian and harmonic oscillations are also studied with the applications of quasi-periodic oscillations (QPOs) where we proposed a method to test gravity theories through data from astrophysical observations of twin-peak QPOs in relativistic precession (RP) model. Finally, we show the dependence of the distance from the central BH to the orbit where twin-peak QPOs shine from the spin of Kerr BH, magnetic charge of Bardeen and Reissner–Nordström (RN) BHs, and GB coupling parameter.

In this paper, we present a quantum description of black holes given by coherent states of gravitons sourced by a matter core. The expected behavior in the weak-field region outside the horizon is recovered, with arbitrarily good approximation, but the classical central singularity is not resolved because the coherent states may not contain modes of arbitrarily short wavelength and the matter core must therefore have finite size. Ensuing quantum corrections both in the interior and exterior is also estimated by assuming that the mean-field approximation holds everywhere. These deviations from the classical black hole geometry can be viewed as quantum hair and will lead to a quantum corrected horizon radius and thermodynamics.

In this paper, we obtain a new class of stationary axisymmetric spacetimes by using the Gürses–Gürsey metric with an appropriate mass function in order to generate a rotating core of matter that may be smoothly matched to the exterior Kerr metric. The same stationary spacetimes may be obtained by applying a slightly modified version of the Newman–Janis algorithm to a nonrotating spherically symmetric seed metric. The starting spherically symmetric configuration represents a nonisotropic de Sitter-type fluid whose radial pressure $p_r$ satisfies an state equation of the form $p_r=-\rho$, where the energy density $\rho$ is chosen to be the Tolman-type-VII energy density [R. C. Tolman, Phys. Rev.55, 364 (1939)]. The resulting rotating metric is then smoothly matched to the exterior Kerr metric, and the main properties of the obtained geometries are investigated. All the solutions considered in this study are regular in the sense they are free of curvature singularities. Depending on the relative values of the total mass m and rotation parameter a, the resulting stationary spacetimes represent different kinds of rotating compact objects such as regular black holes, extremal regular black holes, and regular starlike configurations.

Two interesting hypotheses about black holes have been proposed. The older one states that microscopic black holes can be accountable for the observed dark matter density. The newer one states that black holes are coupled to the expansion of the universe. Here, we combine those ideas and investigate the behavior of expanding microscopic black holes. We observe two temperatures at which the radiation balances the expansion. While one of the balance points might be important in the analysis of primordial scenarios, the other would lead to a strong diffuse gamma radiation background, which is contradicted by the lack of observations. This establishes another indirect evidence disfavoring the hypothesis of cosmological coupling of black holes.

In this paper, we explore the characteristics of two novel regular spacetimes that exhibit a nonzero vacuum energy term, under the form of a (quasi) anti-de Sitter phase. Specifically, the first metric is spherical, while the second, derived by applying the generalized Newman–Janis algorithm to the first, is axisymmetric. We show that the equations of state of the effective fluids associated with the two metrics asymptotically tend to negative values, resembling quintessence. In addition, we study test particle motions, illustrating the main discrepancies among our models and more conventional metrics exhibiting non-vanishing anti-de Sitter phase.

We study the absorption cross section of a massless test scalar field, for arbitrary frequency values, in the background of an Ayón-Beato-García electrically charged regular black hole spacetime. We show that Ayón-Beato-García regular black holes can mimic the absorption properties of Reissner-Nordström black holes in the whole frequency range, for small-to-moderate values of the normalized electric charge.