Regular black holes in UV self-complete quantum gravity

To have the correct picture of a black hole as a whole, it is of crucial importance to understand its interior. The singularities that lurk inside the horizon of the usual Kerr-Newman family of black hole solutions signal an endpoint to the physical laws and, as such, should be substituted in one way or another. A proposal that has been around for sometime is to replace the singular region of the spacetime by a region containing some form of matter or false vacuum configuration that can also cohabit with the black hole interior. Black holes without singularities are called regular black holes. In the present work, regular black hole solutions are found within general relativity coupled to Maxwell's electromagnetism and charged matter. We show that there are objects which correspond to regular charged black holes, whose interior region is de Sitter, whose exterior region is Reissner-Nordstr\"om, and the boundary between both regions is made of an electrically charged spherically symmetric coat. There are several types of solutions: regular nonextremal black holes with a null matter boundary, regular nonextremal black holes with a timelike matter boundary, regular extremal black holes with a timelike matter boundary, and regular overcharged stars with a timelike matter boundary. The main physical and geometrical properties of such charged regular solutions are analyzed.

We study solutions in non-linear electrodynamics (NED) and establish several general results. We show, that the SO(2) electric-magnetic duality symmetry is restrictive enough to allow for reconstruction of the NED Lagrangian from the spherically-symmetric electrostatic (Coulomb-like) solution — although there are infinitely many different NED theories admitting a given solution, there exists a unique SO(2) invariant one among them under a simple analyticity assumption (that leaves out some interesting physical theories). We introduce a general algorithm for constructing new SO(2) invariant NED theories in the conventional approach, where only a few examples are available. We also show how to derive the Lagrangian of the SO(2) invariant theory admitting a given electrostatic solution. We further show on a simple example that some NED theories may require sources (particles) of finite (non-zero) size. Such a non-zero size source not only regularizes the infinite energy of the point charge but also satisfies the condition of regularity, that the electric field is zero at the origin. The latter condition was identified earlier as necessary and sufficient for the NED solution to generate a regular black hole via so-called double copy construction and is also satisfied by solitons. We propose a large class of solitonic NED solutions that give rise to regular black holes via double copy construction and contain solutions of Maxwell and Born-Infeld as different limits. This class of NED solutions acquires two new properties in the limit where the corresponding regular black hole’s asymptotics becomes Minkowski: it gives rise to regular higher-spin black holes via generalization of double copy — “higher-copy” construction, and for very short distances changes the sign of the force becoming repulsive/attractive for opposite/similar signs of charges.

We classify all fundamental electrically charged thin shells in general relativity, i.e., static spherically symmetric perfect fluid thin shells with a Minkowski spacetime interior and a Reissner-Nordstr\"om spacetime exterior, characterized by the spacetime mass and electric charge. The fundamental shell can exist in three states, nonextremal, extremal, and overcharged. The nonextremal state allows the shell to be located such that its radius can be outside its own gravitational radius, or can be inside its own Cauchy radius. The extremal state allows the shell to be located such that its radius can be outside its own gravitational radius, or can be inside it. The overcharged state allows the shell to be located anywhere. There is a further division, one has to specify the orientation of the shell, i.e., whether the normal out of the shell points toward increasing or decreasing radii. There is still a subdivision in the extremal state when the shell is at the gravitational radius, in that the shell can approach it from above or from below. The shell is assumed to be composed of an electrically charged perfect fluid, and the energy conditions are tested. Carter-Penrose diagrams are drawn for the shell spacetimes. There are fourteen cases in the classification of the fundamental shells, namely, nonextremal star shells, nonextremal tension shell black holes, nonextremal tension shell regular and nonregular black holes, nonextremal compact shell naked singularities, Majumdar-Papapetrou star shells, extremal tension shell singularities, extremal tension shell regular and nonregular black holes, Majumdar-Papapetrou compact shell naked singularities, Majumdar-Papapetrou shell quasiblack holes, extremal null shell quasinonblack holes, extremal null shell singularities, Majumdar-Papapetrou null shell singularities, overcharged star shells, and overcharged compact shell naked singularities.

As argued in [78], introducing a non-minimally coupled scalar field, three-dimensional Einstein gravity can be extended by infinite families of theories which admit simple analytic generalizations of the charged BTZ black hole. Depending on the gravitational couplings, the solutions may describe black holes with one or several horizons and with curvature or BTZ-like singularities. In other cases, the metric function behaves as f (r) $$ \overset{\left(r\to 0\right)}{\sim } $$ ∼ r → 0 $$ \mathcal{O}\left({r}^{2s}\right) $$ O r 2 s with s ≥ 1, and the black holes are completely regular — a feature unique to three dimensions. Regularity arises generically i.e., without requiring any fine-tuning of parameters. In this paper we show that all these theories satisfy Birkhoff theorems, so that the most general spherically-symmetric solutions are given by the corresponding static black holes. We perform a thorough characterization of the Penrose diagrams of the solutions, finding a rich structure which includes, in particular, cases which tessellate the plane and others in which the diagrams cannot be drawn in a single plane. We also study the motion of probe particles on the black holes, finding that observers falling to regular black holes reach the center after a finite proper time. Contrary to the singular cases, the particles are not torn apart by tidal forces, so they oscillate between antipodal points describing many-universe orbits. We argue that in those cases the region r = 0 can be interpreted as a horizon with vanishing surface gravity, giving rise to generic inner-extremal regular black hole solutions. We also analyze the deep interior region of the solutions identifying the presence of Kasner eons and the conditions under which they take place. Finally, we construct new black hole solutions in the case in which infinite towers of terms are included in the action.

We analyze the effects of thermal fluctuations on a regular black hole (RBH) of the non-minimal Einstein–Yang–Mill theory with gauge field of magnetic Wu–Yang type and a cosmological constant. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations corresponding to non-minimal RBH thermodynamics. In this scenario, we develop various important thermodynamical quantities, such as entropy, pressure, specific heats, Gibb’s free energy and Helmholtz free energy. We investigate the first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal RBH. We also discuss the stability of this RBH using various frameworks such as the gamma factor (the ratio of heat capacities), phase transition, grand canonical ensemble and canonical ensemble. It is observed that the non-minimal RBH becomes globally and locally more stable if we increase the value of the cosmological constant.

We obtain an exact solution of $AdS$ black hole solution in Einstein-Gauss-Bonnet (EGB) gravity coupled with nonlinear electrodynamics. It interpolates with the $AdS$ regular black hole and $AdS$ EGB black hole in the absence of the Gauss-Bonnet coupling constant and both magnetic monopole charge and deviation parameter, respectively. Based on horizon thermodynamics, we study the thermodynamic properties of the obtained solution (e.g. mass, temperature, entropy, heat capacity and free energy). The Hawking temperature of the nonsingular black hole gets the maximum value at the point where specific heat diverges and the second-order phase transition occurs at the same point. We find that the smaller nonsingular black holes are stable due to positive heat capacity and negative free energy. We explicitly trace the relations between the black hole shadow and the critical behavior of charged EGB $AdS$ regular black hole in the extended phase space.

In this work, we discuss the accretion onto static spherical symmetric regular black holes for specific choices of equation of state parameter. The underlying regular black holes are charged regular black hole using Fermi-Dirac Distribution, logistic distribution, nonlinear electrodynamics, respectively and Kehagias-Sftesos asymptotically flat regular black hole. We obtain the critical radius, critical speed and squared sound speed during the accretion process near the regular black holes. We also study the behavior of radial velocity, energy density and rate of change of mass for each regular black holes.

We find a new black hole in three-dimensional anti-de Sitter space by introducing an anisotropic perfect fluid inspired by the noncommutative black hole. This is a regular black hole with two horizons. We compare the thermodynamics of this black hole with that of a non-rotating BTZ black hole. The first-law of thermodynamics is not compatible with the Bekenstein–Hawking entropy.

In this thesis, the author studies the information loss problem using semi-classical black holes. If a black hole loses information after evaporation, it will imply the violation of unitarity and predictability. Therefore, to understand the nature of the Theory of Everything and to reconcile the quantum theory and gravitation, we need to understand the problem of the information loss. If we assume that there exists a unitary theory of quantum gravity as a working hypothesis, the area of a black hole is proportional to the statistical entropy of the black hole, and there is an observer who can see information from Hawking radiation, then it is inevitable to accept black hole complementarity. However, if there is an observer who can see both information of inside and outside, i.e., if the duplication experiment is possible, then black hole complementarity will be violated. A duplication experiment and other thought experiments can be investigated by semi-classical backgrounds. In this thesis, we focus on three subjects: gravitational objects of Einstein gravity with renormalized energy-momentum tensors, gravitational objects of modified theories of gravity, and initial conditions which can be prepared by quantum tunneling. To study such subjects, we use the following techniques: traditional analytic approaches, numerical approaches using the double-null formalism, and Euclidean analytic continuations. We study a possibility of a duplication experiment in a charged black hole and a regular black hole. Causal structures allow the possibility; but to regularize curvatures around the inner horizon, we require a sufficiently large number of massless fields which contribute to Hawking radiation. In fact, if we assume the large number, we can violate black hole complementarity even for neutral black holes. The required number of fields can be reduced to a reasonable amount; although we need a large number, if it is finite, the number may be allowed by a model of quantum gravity including string theory. This suggests that the area of the black hole may not imply the statistical entropy of the internal and physical degrees of freedom and there may be no observer who can read information via Hawking radiation. Also, we study a possibility of a formation of a bubble universe. The author used weaker assumptions than previous authors to obtain bubble universes. The Brans-Dicke theory can allow a false vacuum bubble as an instanton solution and such a theory may be allowed by quantum gravity including string theory. False vacuum bubbles will emit negative energy along the out-going direction and such negative energy can be used to obtain a bubble universe. Although we have to check whether these scenarios are possible in realistic quantum gravity, if it is possible, then it will strongly support a loss of information and a violation of unitarity at least in the ‘effective’ sense. These conclusions imply that, if there exists a unitary theory of quantum gravity or the Theory of Everything, we will observe a lose of information and a violation of unitarity in the ‘effective’ way.

<p>Various spacetime candidates for traversable wormholes, regular black holes, and ‘black-bounces’ are presented and thoroughly explored in the context of the gravitational theory of general relativity. All candidate spacetimes belong to the mathematically simple class of spherically symmetric geometries; the majority are static (time-independent as well as nonrotational), with a single dynamical (time-dependent) geometry explored. To the extent possible, the candidates are presented through the use of a global coordinate patch – some of the prior literature (especially concerning traversable wormholes) has often proposed coordinate systems for desirable solutions to the Einstein equations requiring a multi-patch atlas. The most interesting cases include the so-called ‘exponential metric’ – well-favoured by proponents of alternative theories of gravity but which actually has a standard classical interpretation, and the ‘black-bounce’ to traversable wormhole case – where a metric is explored which represents either a traversable wormhole or a regular black hole, depending on the value of the newly introduced scalar parameter a. This notion of ‘blackbounce’ is defined as the case where the spherical boundary of a regular black hole forces one to travel towards a one-way traversable ‘bounce’ into a future reincarnation of our own universe. The metric of interest is then explored further in the context of a time-dependent spacetime, where the line element is rephrased with a Vaidya-like time-dependence imposed on the mass of the object, and in terms of outgoing/ingoing EddingtonFinkelstein coordinates. Analysing these candidate spacetimes extends the pre-existing discussion concerning the viability of non-singular black hole solutions in the context of general relativity, as well as contributing to the dialogue on whether an arbitrarily advanced civilization would be able to construct a traversable wormhole.</p>

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.

Investigating the motion of matter near black holes (BHs) provides a powerful avenue to probe the extremes of gravity and the foundational properties of spacetime. This study explores in detail the motion of test particles in the vicinity of a static, spherically symmetric regular BH, defined by two key parameters: the mass [Formula: see text] and a spacetime deformation factor [Formula: see text]. Through an effective potential approach, we derive exact analytical expressions for the energy and angular momentum of particles on circular orbits, revealing how orbital stability is influenced by deviations from the Schwarzschild geometry. Our analysis encompasses the innermost stable circular orbits (ISCOs) and the associated dynamical forces acting on test particles, offering critical insights into the structure of the BH’s near-horizon geometry. We extend our analysis to the numerical integration of the geodesic equations, revealing intricate orbital structures such as epicyclic motion confined to the equatorial plane. Additionally, we derive closed-form expressions for the radial, vertical, and orbital frequencies, all expressed explicitly in terms of the deformation parameter [Formula: see text], allowing for direct confrontation with observational QPO data. We also investigate the periastron precession frequency and demonstrate how these frequency modes may serve as observational probes of the underlying spacetime. Finally, we analyze particle collisions near the event horizon, calculating the center-of-mass energy to assess the potential for high-energy interactions in regular BH environments. These results offer a unified framework for connecting BH geometry, particle dynamics, and QPO observables, advancing our understanding of both theoretical and astrophysical aspects of regular BHs.

The thermodynamics for regular black holes (RBHs) is considered under the restricted phase space (RPS) formalism. It is shown that the RPS formalism seems to hold for RBHs, however, in order for the extensive thermodynamic parameters to be independent from each other, the RBHs need to be viewed as intermediate thermodynamic states in a larger class of black holes (BHs) which admit both regular and singular states. This idea is checked for several classes of BHs. In particular, for the electrically charged Hayward class BHs, it is shown that the regular states can either be thermodynamically stable or unstable, depending on the amount of charges carried by the BHs. The quasinormal frequencies for the Hayward class BHs are also analyzed, and it turns out that, even for the thermodynamically unstable regular states, the dynamic stability still holds, at least under massless scalar perturbations.

With the recent release of the black hole image of Sgr A* alongside the earlier image of M87*, one can now really hope to acquire a better understanding of the gravitational physics at the horizon scale. In this paper, we investigate the prospect of the regular black hole scenario with a Minkowski core in explaining the observed shadow of M87* and Sgr A*. Regular black holes generally appear in Einstein gravity coupled to non-linear electrodynamics and are interesting as they can evade the r = 0 curvature singularity arising in general relativity. Using the previously determined mass and distance we compute the observables associated with the black hole shadow. These when compared with the observed angular diameter reveals that the shadow of M87* and Sgr A* favor the regular black hole scenario with a small but non-zero charge. The implications are discussed.

We study scalar test-field perturbations on top of a Kerr--black-bounce background, i.e. a family of rotating regular black holes and/or rotating traversable wormholes that can mimic Kerr black holes. We compute the quasi-normal modes for a massless field in both the regular black holes and wormhole branches, confirming the stability of the former and identifying a set of growing modes that renders the latter unstable. We further compute the superradiance amplification factors, for massless and massive fields, in the regular black hole branch, confirming that these objects superradiate, though to a lesser degree than the corresponding Kerr black holes.