Regular Black Hole Solutions Research Articles

Minimally deformed regular Bardeen black hole solutions in Rastall theory

In this study, we utilize the minimal geometric deformation technique of gravitational decoupling to extend the regular Bardeen black hole, leading to the derivation of new black hole solutions within the framework of Rastall theory. By decoupling the field equations associated with an extended matter source into two subsystems, we address the first subsystem using the metric components of the regular Bardeen black hole. The second subsystem, incorporating the effects of the additional source, is solved through a constraint imposed by a linear equation of state. By linearly combining the solutions of these subsystems, we obtain two extended models. We then explore the distinct physical properties of these models for specific values of the Rastall and decoupling parameters. Our investigations encompass effective thermodynamic variables such as density and anisotropic pressure, asymptotic flatness, energy conditions, and thermodynamic properties including Hawking temperature, entropy, and specific heat. The results reveal that both models violate asymptotic flatness of the resulting spacetimes. The violation of energy conditions indicate the presence of exotic matter, for both models. Nonetheless, the energy density, radial pressure, as well as the Hawking temperature exhibit acceptable behavior, while the specific heat and Hessian matrix suggest thermodynamic stability.

Dymnikova black hole from an infinite tower of higher-curvature corrections

Recently, in [1], it was demonstrated that various regular black hole metrics can be derived within a theory featuring an infinite number of higher curvature corrections to General Relativity. Moreover, truncating this infinite series at the first few orders already yields a reliable approximation of the observable characteristics of such black holes [2]. Here, we further establish the existence of another regular black hole solution, particularly the D-dimensional extension of the Dymnikova black hole, within the equations of motion incorporating an infinite tower of higher-curvature corrections. This solution is essentially nonperturbative in the coupling parameter, rendering the action, if it exists, incapable of being approximated by a finite number of powers of the curvature. In addition, we compute the dominant quasinormal frequencies of such black holes using both the Bernstein polynomial method and the 13th order WKB method with Padé approximants, obtaining a high degree of agreement between them.

Accretion disks properties around regular black hole solutions obtained from non-linear electrodynamics

We investigate a family of spherically symmetric, static, charged regular black hole solutions derived within the framework of Einstein-nonlinear electrodynamics. Our study focuses on examining the characteristics of accretion disks in the spacetimes described by the Dymnikova and Fan-Wang solutions. We explore circular geodesics of test particles and calculate various properties, including the radius of the innermost stable circular orbit, radiant energy, temperature, and conversion efficiency of accretion mass into radiation. We employ the Novikov-Thorne-Page thin accretion disk model as a background. By comparing our findings with those obtained in the Schwarzschild black hole case, we reveal significant modifications in the overall spectral properties. Specifically, we observe an increase in the energy emitted from the disk surface, resulting in higher temperatures for the accretion disks under certain values of the free parameters. Consequently, we note an enhanced efficiency of mass conversion into radiation compared to the Schwarzschild spacetime.

Lagrangian reverse engineering for regular black holes

Nonlinear extensions of classical Maxwell's electromagnetism are among the prominent candidates for theories admitting regular black hole solutions. A quest for such examples has been fruitful, but mostly unsystematic and littered by the introduction of physically unrealistic Lagrangians. We provide a procedure which admits the reconstruction of a nonlinear electromagnetic Lagrangian, consistent with the Euler–Heisenberg Lagrangian in the weak-field limit, from a given metric representing a regular, magnetically charged black hole.

Gaussian black holes in brane-world model

We present regular black hole solutions in the framework of Brane-world gravity sourced by a Gaussian matter distribution. The black hole metric shares all the common features of regular black holes in the modified General Relativity (GR) with some exciting features. Considering the energy momentum tensor for an isotropic fluid on the brane, the modified Einstein field equation results with an effective energy momentum tensor that describes an anisotropic fluid determined by brane world parameters. Although the effective radial pressure and energy density satisfy the vacuum energy condition, the effective transverse pressure behaves differently. Gaussian black hole (GBH) solutions are obtained from a Gaussian matter distribution. In the paper, a new class of GBH solutions are obtained in the brane-world gravity with effective normal matter in addition to exotic matter distribution. In the brane world gravity, the mass of a GBH depends on the brane tension. The mass of a GBH formed in the brane world is greater than that at low energy (i.e., GR). We study the trajectories of the massive and the massless particles that can be trapped around a GBH for a set of model parameters. The radii of the photon spheres around the GBH and the condition for the stability of the trajectories of the photon spheres are determined. The properties of the GBHs are studied in detail, including their possible observable features.

Extension of Hayward black hole in [formula omitted] gravity coupled with a scalar field

This study looks into regular black hole solutions in a theory of gravity called f(R) gravity, which also involves a scalar field. The f(R) theory changes Einstein’s ideas by adding a new function related to something called the Ricci scalar. This lets us tweak the equations that describe how gravity works. Adding a scalar field makes the theory more interesting, giving us more ways to investigate and understand it. The main goal of this research is to create regular black holes using a combination of f(R) gravitational theory and a scalar field. Regular solutions do not have any singularities, which are points where certain physical quantities, like invariants, become really big or undefined. In this context, we find two regular black hole solutions by using a spherical space with either an equal or unequal approach. For the solutions where we use the equal approach, we figure out the shape of f(R) and how it changes, along with its first and second derivatives. We demonstrate that Hayward’s solution in this theory stays steady because all the shapes of f(R) and their first and second derivatives are positive. Next, we focus on the case where the metric is not equal and figure out the black hole solution. We also find out what f(R) and the scalar field look like in this situation. We demonstrate that the solution in this case is a broader version of the Hayward solution. When certain conditions are met, we end up back at the scenario where the metrics are equal. We also prove that this model is stable because f(R), along with its first and second derivatives, are all positive. We analyze the trajectories of these black hole solutions and determine the forms of their conserved quantities that remain same along those trajectories.

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.

(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.

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.

Dynamics and kinetics of phase transition for regular AdS black holes in general relativity coupled to nonlinear electrodynamics

We study the stochastic dynamics and kinetics of the phase transition of the regular black holes in Anti-de Sitter spacetime by employing the free energy landscape. Our investigation focuses on two important classes of regular black hole solutions, namely the Hayward and Bardeen, which can be obtained from coupling of non-linear electrodynamics. The dynamics of the phase transition is described by the Fokker–Planck equation, using which, we investigate the probabilistic evolution of regular AdS black holes. We solve this equation numerically by imposing both reflecting and absorbing boundary conditions and appropriate initial conditions. In this context, the on-shell Gibbs free energy is treated as a function of the event horizon radius, where the difference of the event horizon radii in different phases serves as the order parameter for the phase transition. The study allows us to probe the dynamic process of transitioning between coexisting small and large black hole phases due to thermal fluctuations, as quantified by the calculation of the first passage time. Furthermore, we explore the influence of temperature on this dynamic process. This research contributes to a deeper understanding of the microstructures of regular AdS black holes.

Black Hole Solutions with Dark Matter Halos in the Four‐Dimensional Einstein‐Gauss‐Bonnet Gravity

AbstractBlack holes (BHs) convey information about different matter‐energy distributions in their immediate environment, as they bear the imprints of the intrinsic spacetime geometry and exotic surrounding matter. In this regard, exact spherically symmetric regular black hole (BH) solutions supported by two phenomenological distributions of dark matter galactic halos in Eintein‐Gauss‐Bonnet gravity are explored. Analytical solutions for the metric and the corresponding thermodynamic properties, including heat capacity (), Gibbs' free energy (), and Hawking temperature () associated with the BH's horizon radius and quasinormal modes (QNMs) are found. The specific heat is investigated, and it is discovered that a Hawking‐Page phase transition with divergent occurred at a critical radius, . Consequently, the authors have regular BHs with Cauchy and event horizons, and evaporation results in thermodynamically stable double‐horizon BH remnants with zero temperatures. The QNMs of the scalar field perturbations on the regular background of the BHs are then discussed comprehensively.

A new class of regular black holes in Einstein Gauss-Bonnet gravity with localized sources of matter

We provide a new regular black hole solution (RBH) in Einstein Gauss-Bonnet (EGB) gravity with localized sources of matter in the energy–momentum tensor. We determine the necessary constraints in order for the solution to be regular. Although we use a specific form for the energy density as a test of proof, these constraints could serve as a recipe for constructing several new RBH solutions in EGB gravity with localized sources. Due to that the usual first law of thermodynamics is not valid for RBH, so we rewrite the first law for EGB, which leads to correct values of entropy and volume. The size of the extremal black hole, whose temperature vanishes, becomes smaller for larger dimensions, whose radius could be of the order of the Planck units, thus the evaporation would stop once the horizon radius contracts up to a value close to the Planck length, which could be related with the apparition of quantum effects. Furthermore, the presence of matter fields in the energy–momentum tensor induces two phase transitions, where there are two regions of stability. This differs from the vacuum EGB solution, where the specific heat is always negative without phase transition as occurs in Schwarzschild black hole.

New regular 2+1 black hole solutions in bilocal gravity

We obtain new regular black hole solutions for an action in 2+1 dimensions with a bilocal Ricci scalar and a negative cosmological constant. Besides their connection to the cosmological constant, these solutions depend on a fundamental length due to their nonlocal nature. The effective profile densities that result from the nonlocal geometries have quasi-localized mass/energy since they are finite at the origin and their integration in all space is convergent. The black holes obtained are free of singularities and present one, two, or none horizons depending on the values of the involved parameters. The new solutions can have either an AdS, dS, or even a flat core. In the case of a de-Sitter core, it could represent a repulsive force coming from quantum effects. Although the resulting (effective) cosmological constant is positive near the origin, the classical (naked) counterpart is still negative thus precluding a cosmological horizon. We investigate the energy conditions of the effective source and determine the region where exotic energy should be found. Thermodynamic quantities are also computed. On the one hand, the Gibbs’s potential shows that both solutions are globally unstable, as in the BTZ case. On the other hand, we show that for small values of the horizon radius the Hawking temperature is negatively divergent but a finite size remnant can be defined where [Formula: see text] crosses zero. At this point, the heat capacity sign changes from negative to positive, indicating that the black holes are locally stable while irradiating. Thus, such a quantity, along with [Formula: see text] presents crucial differences with the BTZ black hole for small horizon radii where quantum effects become relevant. Finally, we analyze the bilocal black hole geodesics and find stable circular orbits for massless and massive particles, another feature absent in the BTZ case.

Quasinormal modes and phase structure of regular AdS Einstein–Gauss–Bonnet black holes

In this paper, we present an exact regular black hole solution in Einstein–Gauss–Bonnet coupled with nonlinear matter fields. It is a generalization of a regular Einstein–Gauss–Bonnet black hole in [Formula: see text] [Formula: see text] spacetime. The causal structure of the obtained solution identifies with Boulware–Deser black hole solution, except for the curvature singularity at the center. It incorporates the Boulware–Deser black holes in the absence of deviation parameters. We also study the thermodynamic properties of the solution that satisfies a modified first law of thermodynamics. Furthermore, we discuss the stability of the obtained black hole solution and, in this regard, a double phase transition occurs. Within this context, we find that phase transition exists at the point where the heat capacity diverges and, incidentally, the temperature attains the maximum value. We discuss the fluid nature of the black hole also exhibiting critical points. The quasinormal modes of the black hole solution and their dependencies on Gauss–Bonnet coupling and deviation parameters are also analyzed in terms of null geodesics.

A new class of anisotropic rotating fluids and some throat-like sources for Kerr metric as examples

Motivated by the increasing interest in finding physically viable rotating sources, we present a new class of anisotropic rotating solutions. The energy–momentum tensor compatible with the metric is composed of anisotropic matter with a nonvanishing energy flow around the symmetry axis and vanishing viscosity. The new class of solutions can be used to find new possible sources for the Kerr metric, to obtain new regular black hole solutions and to study galaxies with a central rotating black hole and an halo of dark matter. As an example, we obtain a five-parameter class of solutions representing a two-way traversable wormhole smoothly matched to the Kerr one and satisfying all energy conditions outside the wormhole for a wide range of parameters, in particular for compact objects. Finally, with a simple modification of the aforementioned solution, we obtain a source for Kerr metric with a throat geometry, nonrepresenting a two-way traversable wormhole and satisfying all energy conditions.

Stationary black holes and stars in the Brans-Dicke theory with Λ&gt;0 revisited

It was shown a few years back that for a stationary regular black hole or star solution in the Brans-Dicke theory with a positive cosmological constant $\mathrm{\ensuremath{\Lambda}}$, endowed with a de Sitter or cosmological event horizon in the asymptotic region, not only there exists no nontrivial field configurations, but also the inverse Brans-Dicke parameter ${\ensuremath{\omega}}^{\ensuremath{-}1}$ must be vanishing. This essentially reduces the theory to Einstein's general relativity. The assumption of the existence of the cosmological horizon was crucial for this proof. However, since the Brans-Dicke field $\ensuremath{\phi}$, couples directly to the $\mathrm{\ensuremath{\Lambda}}$-term in the energy-momentum tensor as well as $\mathrm{\ensuremath{\Lambda}}$ acts as a source in $\ensuremath{\phi}$'s equation of motion, it seems reasonable to ask: can $\ensuremath{\phi}$ become strong instead and screen the effect of $\mathrm{\ensuremath{\Lambda}}$, at very large scales, so that the asymptotic de Sitter structure is replaced by some alternative, yet still acceptable boundary condition? In this work we analytically argue that no such alternative exists, as long as the spacetime is assumed to be free of any naked curvature singularity. We further support this result by providing explicit numerical computations. Thus we conclude that in the presence of a positive $\mathrm{\ensuremath{\Lambda}}$, irrespective of whether the asymptotic de Sitter boundary condition is imposed or not, a regular stationary black hole or even a star solution in the Brans-Dicke theory always necessitates ${\ensuremath{\omega}}^{\ensuremath{-}1}=0$, and thereby reducing the theory to general relativity. The qualitative differences of this result with that of the standard no hair theorems are also pointed out.

Regular black holes in Verlinde’s emergent gravity

In this paper, we construct a class of charged and regular black hole solutions in Verlinde’s Emergent Gravity (VEG). In particular, these solutions include, black holes with asymptotically Minkowski core, T-duality, Frolov/Simpson–Visser type solutions, as well as the Bardeen/Hayward type solutions as a special case. Using the relation between the apparent dark matter and the baryonic matter we find the effect of apparent dark matter on the spacetime geometry. We show that in general, the apparent dark matter leads to non-asymptotically flat spacetime geometry and, in the special limit of a point like mass distribution, all the black hole solutions in VEG resembles the global monopole-like solution with a deficit angle. To this end, we extend the solutions by including the cosmological constant (de Sitter space) and we elaborate different energy conditions of black hole solutions. Finally, having in mind that the Einstein’s field equation are not modified in this theory while the apparent dark matter is encoded in the energy–momentum tensor, we used the modified Newman–Janis-Azreg-Aïnou algorithm to obtain the corresponding effective rotating metrics.

A new class of regular black hole solutions with quasi-localized sources of matter in (2 + 1) dimensions

This paper investigates a new class of regular black hole solutions in (2 + 1)-dimensions by introducing a generalization of the quasi-localized matter model proposed by Estrada and Tello-Ortiz. Initially, we try to physically interpret the matter source encoded in the energy-momentum tensor as originating from nonlinear electrodynamics. We show, however, that the required conditions for the quasi-locality of the energy density are incompatible with the expected behavior of nonlinear electrodynamics, which must tend to Maxwell's theory on the asymptotic limit. Despite this, we propose a generalization for the quasi-localized energy density that encompasses the existing models in the literature and allows us to obtain a class of regular black hole solutions exhibiting remarkable features on the event horizons and their thermodynamic properties. Furthermore, since the usual version of the first law of thermodynamics, due to the presence of the matter fields, leads to incorrect values of entropy and thermodynamics volume for regular black holes, we propose a new version of the first law for regular black holes.

Charged black holes from T-duality

In this paper, we present a family of regular black hole solutions in the presence of charge and angular momentum. We also discuss the related thermodynamics and we comment about the black hole life cycle during the balding and spin down phases. Interestingly the static solution resembles the Ayón-Beato–García spacetime, provided the T-duality scale is redefined in terms of the electric charge, l0→Q. The key factor at the basis of our derivation is the employment of Padmanabhan's propagator to calculate static potentials. Such a propagator encodes string T-duality effects. This means that the regularity of the spacetimes here presented can open a new window on string theory phenomenology.

Rotational Energy Extraction from the Kerr Black Hole’s Mimickers

In this paper, the Penrose process is used to extract rotational energy from regular black holes. Initially, we consider the rotating Simpson–Visser regular spacetime, which describes the class of geometries of Kerr black hole mimickers. The Penrose process is then studied through conformally transformed rotating singular and regular black hole solutions. Both the Simpson–Visser and conformally transformed geometries depend on mass, spin, and an additional regularisation parameter l. In both cases, we investigate how the spin and regularisation parameter l affect the configuration of an ergoregion and event horizons. Surprisingly, we find that the energy extraction efficiency from the event horizon surface is not dependent on the regularisation parameter l in the Simpson–Visser regular spacetimes, and hence, it does not vary from that of the Kerr black hole. Meanwhile, in conformally transformed singular and regular black holes, we obtain that the efficiency rate of extracted energies is extremely high compared to that of the Kerr black hole. This distinct signature of conformally transformed singular and regular black holes is useful to distinguish them from Kerr black holes in observation.