Solutions in Nonlinear Electrodynamics and their double copy regular black holes

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 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 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.

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 investigate gravitational lensing within the framework of general relativity, focusing particularly on the deflection angle calculations in the weak field limit around a regular charged black hole. The presence of an inherited-centered singularity highlights the complex nature of black holes following gravitational collapse. However, non-linear electrodynamics (NLED) proposes the intriguing concept of a non-singularity, introducing new perspectives to this discussion. Our methodology explicitly incorporates NLED's role in determining the effective geometry of photons, advancing beyond standard metric analyses. The exact solution identifies a new correction term in the deflection angle that is specifically comparable to that of Reissner-Nordstrom (R.N.) model. These distinctive terms in the lensing effects significantly alter the sequence of shifts in the third angular images of a regular charged black hole. This analysis deepens our understanding of the complex interactions between a regular charged black hole and gravitational lensing. Future astronomical observations will be integral to corroborating these theoretically posited models, providing observational validation and potentially elucidating our theoretical framework.

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.

In this work, an exact regular black hole solution in General Relativity is presented. The source is a nonlinear electromagnetic field with the algebraic structure $$ T^{0}_{0}=T^{1}_{1} $$ for the energy–momentum tensor, partially satisfying the weak energy condition but not the strong energy condition. In the weak field limit, the EM field behaves like the Maxwell field. The solution corresponds to a charged black hole with $$q\le 0.77$$ $$\hbox {m}$$ . The metric, the curvature invariants, and the electric field are regular everywhere. The BH is stable against small perturbations of spacetime and using the Weinhold metric, geometrothermodynamical stability has been investigated. Finally we investigate the idea that the observable universe lives inside a regular black hole. We argue that this picture might provide a viable description of universe.

The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In the limiting case where the nonlinear parameter $\beta^2$ goes to infinity, our solution reduces to the Einstein-Maxwell dilaton black holes. We obtain the mass, temperature, entropy and electric potential of these solutions. We also study the behaviour of the electric field as well as the electric potential of these black holes near the origin. We find that the electric field has a finite value \textit{near} the origin, which is the same as the electric field of Born-Infeld nonlinear electrodynamics, but it can diverge exactly at $r=0$ depending on the model parameters. We also investigate the effects of the dilaton field on the behaviour of the electric field and electric potential. Finally, we check the validity of the first law of black hole thermodynamics on the black hole horizon.

In this Letter we investigate the role of regular (curvature singularity-free) black holes in the framework of UV self-complete quantum gravity. The existence of a minimal length, shielding the trans-Planckian regime to any physical probe, is self-consistently included into the black hole probe itself. In this way we obtain to slightly shift the barrier below the Planck length, with the UV self-complete scenario self-consistently confirmed.

In this contribution, we study the quasi-normal modes of a Generic-class of a regular black hole with a magnetic charge in nonlinear electrodynamics, considering scalar and electromagnetic perturbations. The Generic-class contains the Bardeen-class, Hayward-class, and New-class solutions, it can represent a black hole with two horizons or one horizon. First, we obtain the critical values of the magnetic charge and mass; Then, using the third–order WKB approximation, we can determine the dependence of the quasi-normal modes with the parameters of the Generic-class. Finally, the transmission and reflection coefficients of the scattered wave in the third–order WKB approximation are calculated.

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.

<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>

In this work we study regular black holes from a global perspective looking\nfor evading some of the well-known singularity theorems by using their\n"reverses". Then, model geometries for the slices of typical spherically\nsymmetric, (locally) static four dimensional regular black hole solutions are\ndescribed from both an analytical and a topological point of view. While the\nfiniteness of both the scalar and Kretchmann curvature of the slices around the\nregular center determines the geometry of the core, the positive answer to the\nPoincar\\'e conjecture assures that, under two assumptions, its topology is that\nof a three-sphere. However, in general, the cores are shown to be $S^3$, $H^3$,\n$\\mathbb{R}\\times S^1$ or $S^1\\times S^2$, depending whether a de Sitter, anti\nde Sitter, Nariai or Bertotti-Robinson geometries are employed to describe the\nslices at the regular center. Then, a description of the aforementioned slices\nin terms of Seifert fibre spaces is given in order to show that the Euler\ncharacteristic of the bundle can be used to track the transition between the\ncore of the regular black hole and the rest of the slices in most of the cases\nconsidered in the literature. After Geroch and Tipler's theorems are employed\nto study the consequences of topology change on regular black hole spacetimes,\nwe show that Borde and Vilenkin's singularity theorem is used to restrict their\npossible types. We end by noting that Nariai cores can be safely used to\nconstruct regular black holes without topology changes.\n

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.