In this work we construct a family of spherically symmetric, static, charged regular black hole metrics in the context of Einstein-nonlinear electrodynamics theory. The construction of the charged regular black hole metrics is based on three requirements: (a) the weak energy condition should be satisfied, (b) the energy-momentum tensor should have the symmetry $T^{0}_{0}=T^{1}_{1}$, and (c) these metrics have to asymptotically behave as the Reissner-Nordström black hole metric. In addition, these charged regular black hole metrics depend on two parameters which for specific values yield regular black hole metrics that already exist in the literature. Furthermore, by relaxing the third requirement, we construct more general regular black hole metrics which do not behave asymptotically as a Reissner-Nordström black hole metric.
We calculate the entropy of spherically symmetric regular black holes by the path integral and Noether-charge method. Both methods provide an evidence that the entropy of regular black holes should be proportional to quarter of area, and there is no violation of entropy/area law at all.
In this letter, we extend the recent black hole solution with spherical symmetry [Phys. Lett. B \textbf{835} (2022), 137546], to a new class of black hole solutions with different topology, namely, a torus-like black hole and a black string in the presence of the cosmological constant. We have used the regularized expressions for the gravitational and the electromagnetic potentials, then we derived the corrections to the energy density and, finally, the black hole solutions are obtained which are regular in the limit $r \to 0$. Interestingly, it is found that the total mass of the black hole i…
In the framework of Einstein's gravity coupled to nonlinear electromagnetic fields, we study gravito-electromagnetic perturbations of magnetic regular black holes. The master equations of perturbations are obtained through Chandrasekhar's procedure, in which gravitational perturbations with odd-parity are coupled to the electromagnetic perturbations with even-parity. As an application, we apply the master equations to obtain quasinormal modes (QNMs) for three types of regular black holes by using numerical method. Results show that QNMs of regular black holes depends significantly on the param…
We present an exact five-dimensional ($5D$) rotating regular black hole metric, with a deviation parameter $k\geq 0$, that interpolates between the $5D$ Kerr black hole ($k=0$) and $5D$ Kerr-Newman ($r \gg k$). This $5D$ rotating regular black hole is an exact solution of general relativity coupled to nonlinear electrodynamics. Interestingly, for a given value of parameter $k$ there exits a critical angular momentum $a=a_E$ which corresponds to extremal rotating regular black hole with degenerate horizons, while for $a<a_E$, one has non-extremal rotating regular black hole with outer and inner…
In this work, we investigate the static, spherically symmetric regular black hole solutions in a generalized Rastall gravity. In particular, the prescription of Rastall gravity implies that the present approach does not necessarily involve nonlinear electrodynamics. Subsequently, the resulting regular black hole solution can be electrically and magnetically neutral. The general properties of the regular black hole solutions are explored. Moreover, specific solutions are derived and discussed, particularly regarding the parameter related to the degree of violation of energy-momentum conservatio…
We carry quantum (thermal) corrections to the thermodynamics of regular black holes in detail. Firstly, we discuss the non-extended phase space thermodynamics of regular black holes. We obtain expressions for various thermodynamic quantities like temperature, entropy, internal energy, Helmholtz free energy, pressure, enthalpy, and Gibbs free energy. Then we introduce quantum corrections to the thermodynamics of Bardeen type (toy model) of regular black holes. The qualitative and quantitative analysis of these corrections is carried by plotting all the corrected thermodynamic quantities. The co…
The quasinormal modes (QNMs) of a regular black hole with charge are calculated in the eikonal approximation. In the eikonal limit the QNMs of black hole are determined by the parameters of the unstable circular null geodesics. The behaviors of QNMs are compared with QNMs of Reisner-Nordström black hole, it is done by fixing some of the parameters that characterize the black holes and varying another. We observed that the parameter that is related one effective cosmological constant at small distances , determines the behaviors of the QNMs of regular black hole with charge.
The "black-bounce" spacetime geometries, were recently proposed in [A. Simpson, M. Visser, JCAP 02 (2019) 042] as regular black holes that bouncing into a future incarnation of the universe. In this work we will present several black-bounce exact solutions of General Relativity. Among them is a novel type of black-bounce solutions, which in contrast of the Simpson-Visser type [A. Simpson, M. Visser, JCAP 02 (2019) 042], do not have the Ellis wormhole metric as a particular case. The source of these solutions are linear superposition of phantom scalar fields and nonlinear electromagnetic fields…
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…
In this paper, the Penrose process is being 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 the Kerr black hole's mimickers. The Penrose process is then studied through conformally transformed rotating singular and regular black hole solutions. These both 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 $l$ affects the configur…
In this article, the thermodynamics of regular black holes with a cosmic string passing through it is studied. We will observe that the string has no effect on the temperature as well as the relation between entropy S and horizon area A.
We present the generalization of a regular black hole surrounded by quintessence, considering Bardeen-like solutions added with this fluid. We also compare our solution particularized to the Bardeen one with those found in the recent literature, showing that some of them are inconsistent since they add quintessence "by hand", neglecting also the interesting behavior of the complete solution nearby the origin. Then, we present the correct way to implement the quintessential fluid in more general four-dimensional regular black hole geometries and explore some of its consequences, such as removin…
The spacetime singularities in classical general relativity predicted by the celebrated singularity theorems are formed at the end of gravitational collapse. Quantum gravity is the expected theory to resolve the singularity problem, but we are now far from it. Therefore attention has shifted to models of regular black holes free from the singularities. A spherically symmetric regular toy model was obtained by Dymnikova (1992) which we demonstrate as an exact solution of Einstein's field equations coupled to nonlinear electrodynamics for a Lagrangian with parameter $b$ related to magnetic charg…
The existence of a regular non-trivial scalar field in the background of an asymptotically flat static reflecting star is discussed. The scalar field is assumed to be conformally coupled to the outside matter. The induced scalar charge is determined and the required conditions to have regular field are obtained. The results are compared with the case of a black hole. Conditions to have regular non-trivial scalar field out of the black hole horizon are investigated. We show that in the presence of a scalar source, in contrast to the black holes, the reflecting star becomes polarized.
We studied the instability of the regularized 4D charged Einstein-Gauss-Bonnet de-Sitter black holes under charged scalar perturbations. The unstable modes satisfy the superradiant condition, but not all modes satisfying the superradiant condition are unstable. The instability occurs when the cosmological constant is small and the black hole charge is not too large. The Gauss-Bonnet coupling constant makes the unstable black hole more unstable when both the black hole charge and cosmological constant are small, and makes the stable black hole more stable when the black hole charge is large.
The Painlevé-Gullstrand coordinates allow us to explore the interior of the regular Hayward black hole. The behavior of an infalling particle in traversing the Hayward black hole is compared with the one inside the Schwarzschild and Reissner-Nordstrom singular black holes. When approaching the origin the test particle trajectories present differences depending if the center is regular or singular. The velocities of the infalling test particle into the modified Hayward black hole are analyzed as well. As compared with the normal Hayward, in the modified Hayward black hole the particle moves fas…
In this paper, we attempt to study the Joule-Thomson expansion for the regular black hole in an anti-de Sitter background, and obtain the inversion temperature and curve for the Bardeen-AdS black hole in the extended phase space. We investigate the isenthalpic and inversion curves for the Bardeen-AdS black hole in the T-P plane to find the intersection points between them are exactly the inversion points discriminating the heating process from the cooling one. And, the inversion curve for the regular(Bardeen)-AdS black hole is not closed and there is only a lower inversion curve in contrast wi…
The shadow of a black hole can be one of the strong observational evidences for stationary black holes. If we see shadows at the center of galaxies, we would say whether the observed compact objects are black holes. In this paper, we consider a formula for the contour of a shadow in an asymptotically-flat, stationary, and axisymmetric black hole spacetime. We show that the formula is useful for obtaining the contour of the shadow of several black holes such as the Kerr-Newman black hole and rotating regular black holes. Using the formula, we can obtain new examples of the contour of the shadow…
The combined effect of a strong gravitational field and electromagnetic field in the vicinity of a generic regular black hole related to non-linear electrodynamics with Maxwellian weak-field limit on the radiation flux of a hot spot orbiting the regular black hole on the Keplerian disc has been studied. The frequency shift due to the strong gravitational field and magnification of the radiation related to gravitational lensing have been calculated. We compare the flux related to the Maxwellian regular black hole to the flux of the hot spots moving with the same orbital period around standard S…
We consider a particle moving towards a rotating black hole. We are interested in the number of its revolution $n$ around a black hole. In our previous work (Pavlov and Zaslavskii in Gen Relativ Gravit 50: 14, 2018. arXiv:1707.02860) we considered this issue in the Boyer-Lindquist type of coordinates with a subsequent procedure of subtraction. Now, we reconsider this issue using from the very beginning the frames regular on the horizon. For a nonextremal black hole, regularity of a coordinate frame leads to the finiteness of a number of revolutions around a black hole without a subtraction pro…
In the view of the Gliner vacuum, we remove the deformations in the first law of mechanics for regular black holes, where one part of deformations associated with black hole mass will be absorbed into enthalpy or internal energy, and the other part associated with parameters rather than mass will constitute a natural $V$-$P$ term. The improved first law of mechanics redisplays its resemblance to the first law of thermodynamic systems, which implies a restored correspondence of the mechanic variables to the thermodynamic ones. In particular, the linear relation between the entropy and horizon a…
In this work two new families of non-singular or regular black hole solutions are displayed. These black holes behave as de Sitter space near its center and have a well defined AdS asymptotic region for negative cosmological constant. These solutions are constructed on a general ground through the introduction of a finite density of mass/energy. This removes the usual singularity of a black hole and also introduces a new internal geometry. The thermodynamic properties of these solutions are discussed as well.
It is widely believed that the curvature singularities are an artifact of general relativity and may not exist in the Universe, and likely to be defined by the quantum gravity. In the absence of successful quantum gravity, significant attention has been shifted towards the regular models. We present a five-dimensional ($5D$) rotating regular Myers-Perry like black hole metric with two rotation parameters ($a,b$) and a free parameter ($k$). Our $5D$ rotating regular metric encompasses $5D$ Myers-Perry black hole which can be recovered as a special case when $k=0$. The size of the shadow cast by…
We use the monodromy method to investigate the asymptotic quasinormal modes of regular black holes based on the explicit Stokes portraits. We find that, for regular black holes with spherical symmetry and a single shape function, the analytical forms of the asymptotic frequency spectrum are not universal and do not depend on the multipole number but on the presence of complex singularities and the trajectory of asymptotic solutions along the Stokes lines.
Semi-classical corrections at large curvature are employed in toy models of spherically symmetric gravitational collapse in order to avoid the formation of singularities. The resulting spacetimes may produce bounces, compact remnants or regular black holes in place of the usual Schwarzschild black hole. Within these models, a whole class of collapse scenarios leading to the formation of regular black holes may be obtained from General Relativity coupled to some theory of non-linear electrodynamics. In the present chapter we provide a thorough exposition of semi-classical dust collapse with par…
