We study the thermodynamics of the Ayón-Beato-García black hole and the relationship between photon orbits and the thermodynamic phase transitions of the black hole in AdS spacetime. We then examine the interactions between the microstructures of the black hole using Ruppeiner geometry. The radius of the photon orbit and the minimum impact parameter behave non-monotonically below the critical point, mimicking the behaviour of Hawking temperature and pressure in extended thermodynamics. Their changes during the large black hole--small black hole phase transition serve as the order parameter, possessing a critical exponent of $1/2$. The results demonstrate that the gravity and thermodynamics of the Ayón-Beato-García black hole are closely related. Furthermore, we explore the thermodynamic geometry, which provides insight into the microstructure interactions of the black hole. We find that the large black hole phase is analogous to a bosonic gas with a dominant attractive interaction, while the small black hole phase behaves like an anyonic gas with both attractive and repulsive interactions.
In this letter we choose generalized Ayon Beato Gracia (ABG) magnetic charged black hole with five parameters to investigate possibility of thermodynamic phase transition and coexistence of different gass/liquid/solid phases of this black hole. In fact this work is an extension of our recently work where ABG black hole with three parameters was used to seek the phase transition. In this work we obtain other physical values on the parameters with respect to our previous work where the phase transition is happened together with coexistence point of different phases in the phase space.
We study the collision of two particles with equal masses moving in the equatorial plane near horizon of the rotating regular Ayón-Beato-García (ABG) black hole (BH) and calculate the center-of-mass (CM) energy for the colliding particles for both extremal and non-extremal cases. It turns out that CM energy depends not only on rotation parameter $a$ but also on charge $Q$. Particularly for the extremal rotating regular ABG BH, CM energy of two colliding particles could be arbitrarily high for critical angular momentum of particles. Furthermore, we also show that, for a non-extremal BH, there e…
In this paper, we compute quasi-normal modes of ABG black holes (which has a non-linear electrodynamical source) using the WKB methods and AIM. A comparison between the spectrum of QNMs calculated by both methods is made. We analyse how the spectrum of QNMs depends on the black hole parameters, multipole number and overtone number and establish that the ABG black hole is stable against the scalar field.
In this paper, we calculate the effective gravitational mass of Ayón-Beato and Garc\'ıa regular (non-singular) static spherically symmetric asymptotically Minkowskian metric that is a solution to Einstein's equations coupled with a nonlinear electromagnetic field. The effective gravitational mass is negative, zero, or positive that depends on the ratio of magnitude of electric charge to the ADM mass and the ratio of the radial distance to the ADM mass. As expected, at large value of radial distance, our result gives effective gravitational mass of the Reissner-Nordström metric.
In this work we study thermodynamics of generalized Ayon-Beato and Garcia (ABG) black hole metric which contains three parameters named as mass $m$, magnetic charge $q$ and dimensionless coupling constant of nonlinear electrodynamics interacting field $γ$. We showed that central regions of this black hole behaves as dS(AdS) vacuum space by setting $q<2m (q>2m)$ and in the case $q=2m$ reaches to a flat Minkowski space. In the large distances this black hole behaves as a Reissner-Nordstrom BH. However important role of the charge q is appeared in produce of a formal variable cosmological paramet…
We obtain a type of Ayón-Beato-Garc\'ıa (ABG) related black hole solutions with five parameters: the mass $m$, the charge $q$, and three dimensionless parameters $α$, $β$ and $γ$ associated with nonlinear electrodynamics. We find that this type of black holes is regular under the conditions: $αγ\geqslant 6$, $βγ\geqslant 8$, and $γ>0$. Here we focus on the saturated case: $α={6}/γ$ and $β={8}/{γ}$, such that only three parameters $m$, $q$ and $γ$ remain, which leads to a new family of ABG black holes. For such a family of black holes, we investigate the influence of the charge $q$ and the para…
Shape and frequency-shift map of direct and indirect images of Keplerian discs orbiting in Bardeen and Ayon-Beato-Garcia (ABG) black hole and no-horizon spacetimes are determined. Then profiles of spectral lines generated in the innermost parts of the Keplerian discs in the Bardeen and ABG spacetimes are constructed. The frequency-shift maps and profiled spectral lines are compared to those generated in the field of Schwarzschild black holes and possible observationally relevant signatures of the regular black hole and no-horizon spacetimes are discussed. We demonstrate that differences relati…
We obtain the solution of a generalized ABG STVG black hole with the nonlinear tensor field $B_{μν}$ in the scalar-tensor-vector gravity. This black hole is endowed with four parameters, the black hole mass $M$, the parameter $α$ associated with the STVG theory, and the two parameters $λ$ and $β$ that are related to the dipole and quadrupole moments of the nonlinear tensor field, respectively. By analyzing the characteristics of the black hole, we find that the generalized ABG STVG black hole is regular when $λ\geqslant 3$ and $β\geqslant 4$, and we study the effects of the parameters $α$, $λ$…
The rotating Ayón-Beato-García (ABG) black holes, apart from mass ($M$) and rotation parameter ($a$), has an additional charge $Q$ and encompassed the Kerr black hole as particular case when $Q=0$. We demonstrate the ergoregions of rotating ABG black holes depend on both rotation parameter $a$ and charge $Q$, and the area of the ergoregions increases with increase in the values of $Q$, when compared with the Kerr black hole and the extremal regular black hole changes with the value of $Q$. Ban{ã}dos, Silk and West (BSW) demonstrated that an extremal Kerr black hole can act as a particle accele…
Observational Signatures of Rotating Ayón-Beato-García Black Holes: Shadows, Accretion Disks and Images
College of Physics Science and Technology, Hebei University（河北大学物理科学与技术学院）；Hebei Key Lab of Optic-Electronic Information and Materials, Hebei University（河北大学河北省光电信息材料重点实验室）；National-Local Joint Engineering Laboratory of New Energy Photoelectric Devices, Hebei University（河北大学新能源光电器件省部共建国家重点实验室培育基地）；Key Laboratory of High-precision Computation and Application of Quantum Field Theory of Hebei Province, Hebei University（河北大学量子场论高精度计算与应用重点实验室）
We study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and non-linear electrodynamics. They both are characterized by the mass parameter $m$ and the charge parameter $g$. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphe…
We investigate the scattering properties of a massless scalar field in the background of a charged Ayón-Beato-García regular black hole solution. Using a numerical approach, we compute the differential scattering cross section for arbitrary values of the scattering angle and of the incident wave frequency. We compare our results with those obtained via the classical geodesic scattering of massless particles, as well as with the semiclassical glory approximation, and show that they present an excellent agreement in the corresponding limits. We also show that Ayón-Beato-García and Reissner-Nords…
Along the last decades, several regular black hole (BH) solutions, i.e., singularity-free BHs, have been proposed and associated to nonlinear electrodynamics models minimally coupled to general relativity. Within this context, it is of interest to study how those nonlinear-electrodynamic-based regular BHs (RBHs) would interact with their astrophysical environment. We investigate the propagation of a massless test scalar field in the background of an electrically charged RBH solution, obtained by Eloy Ayón-Beato and Alberto García. Using a numerical approach, we compute the absorption cross sec…
We demonstrate that the total energy of electromagnetic field in the Bardeen and Ayón-Beato-García singularity-free models is equal to the mass parameter $M$, being therefore independent of the charge parameter $Q$. Our result is fully congruent with the original idea of Born and Infeld to use nonlinear electrodynamics for proving the electromagnetic nature of mass.
The behavior of the timelike and null geodesics of charged E. Ay$\acute{o}$n-Beato and A. Garcia (ABG) black hole are investigated. For circular and radial geodesics, we investigate all the possible motions by plotting the effective potentials for different parameters. In conclusion, we have shown that there is no phenomenon of \textit{superradiance} in this case.
We introduce a new microscopic quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic quantity is proportional to the macroscopic quantity -- entropy surface density $σ_{S}$, thus connecting a microscopic quantity to a macroscopic quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) tha…
We show that using an adequate coordinate transformation the charged regular black hole solution given by Ayon-Beato and Garcia can be put in the Kerr-Schild form. Then we use this metric in Kerr-Schild Cartesian coordinates with a result given by Virbhadra and obtain the energy distribution associated with this.
We analyze the dynamical stability of black hole solutions in self-gravitating nonlinear electrodynamics with respect to arbitrary linear fluctuations of the metric and the electromagnetic field. In particular, we derive simple conditions on the electromagnetic Lagrangian which imply linear stability in the domain of outer communication. We show that these conditions hold for several of the regular black hole solutions found by Ayon-Beato and Garcia.
Based on the Newman-Janis algorithm the Ayon-Beato-Garcia spacetime metric of the regular spherically symmetric, static and charged black hole has been converted into rotational form. It is shown that the derived solution for rotating regular black hole is regular and the critical value of the electric charge $Q$ for which two horizons merge into one sufficiently decreases in the presence of nonvanishing angular momentum $a$ of the black hole.
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, $l_0\to Q$. 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 th…
We show that the Bronnikov theorem on the nonexistence of regular electrically charged black holes can be circumvented. In the frame of nonlinear electrodynamics, we present the exact regular black hole solutions of a hybrid type. They are electrically charged, but contain a `dual' core confining a polarization of magnetic charges. The considered example is based on a modification of the Ayón-Beato & Garc\'ıa solution. It represents a very specific realization of the idea on confinement based on dual electrodynamics and dual superconductivity.
If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work show that the Bardeen model may also be interpreted as …
We compute the area(or entropy) product formula for a regular black hole derived by Ayón-Beato and García in 1998\cite{abg}. By explicit and exact calculation, it is shown that the entropy product formula of two physical horizons strictly \emph{depends} upon the ADM mass parameter that means it is \emph{not} an universal(mass-independent) quantity. But a slightly more complicated function of event horizon area and Cauchy horizon area is indeed a \emph{mass-independent} quantity. We also compute other thermodynamic properties of the said black hole. We further study the stability of such black …
In this paper, we study quantum corrections to the temperature and entropy of a regular Ayón-Beato-Garc\'ıa-Bronnikov black hole solution by using tunneling approach beyond semiclassical approximation. We use the first law of black hole thermodynamics as a differential of entropy with two parameters, mass and charge. It is found that the leading order correction to the entropy is of logarithmic form. In the absence of the charge, i.e., $e=0$, these corrections approximate the corresponding corrections for the Schwarzschild black hole.
It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarr's formula for the total mass does not. In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole. The same is done for the regular black hole solution derived by Ayon-Beato and Garcia, showing that in the case that variations of the electric charge are involved, the Smarr's formula does not longer is valid.
In this paper we study the thermodynamics and state space geometry of regular black hole solutions such as Bardeen black hole, Ayón-Beato and García black hole, Hayward black hole and Berej-Matyjasek-Trynieki-Wornowicz black hole. We find that all these black holes show second order thermodynamic phase transitions(SOTPT) by observing discontinuities in heat capacity-entropy graphs as well as the cusp type double point in free energy-temperature graph. Using the formulation of geometrothermodynamics we again find the singularities in the heat capacity of the black holes by calculating the curva…
We consider the motion of test particles in the regular black hole space-time given by Ayón-Beato and Garc\'ıa in Phys. Rev. Lett. 80:5056 (1998). The complete set of orbits for neutral and weakly charged test particles is discussed, including for neutral particles the extreme and over-extreme metric. We also derive the analytical solutions for the equation of motion of neutral test particles in a parametric form and consider a post-Schwarzschild expansion of the periastron shift to second order in the charge.
In this paper, we study the weak gravitational lensing in the spacetime of rotating regular black hole geometries such as Ayon-Beato-García (ABG), Bardeen, and Hayward black holes. We calculate the deflection angle of light using the Gauss-Bonnet theorem (GBT) and show that the deflection of light can be viewed as a partially topological effect in which the deflection angle can be calculated by considering a domain outside of the light ray applied to the black hole optical geometries. Then, we demonstrate also the deflection angle via the geodesics formalism for these black holes to verify our…
The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ayón-Beato and Garc{\'ı}a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and …
According to the Einstein, Weinberg, and Møller energy-momentum complexes, we evaluate the energy distribution of the singularity-free solution of the Einstein field equations coupled to a suitable nonlinear electrodynamics suggested by Ayón-Beato and García. The results show that the energy associated with the definitions of Einstein and Weinberg are the same, but Møller not. Using the power series expansion, we find out that the first two terms in the expression are the same as the energy distributions of the Reissner-Nordström solution, and the third term could be used to survey the factual…
We investigate the possibility of arbitrarily high energy in the center of mass(CM) frame of colliding particles in the vicinity of the infinite red-shift surface of the spherically symmetric, static charged regular black holes (Bardeen black hole, Ayón-Beato and García black hole, and Hayward black hole). We show that the CM energy of colliding particles near the infinite red-shift surface of the \emph{extreme} regular black holes are arbitrarily large while the non-extreme regular black holes have the finite energy. We also compute the equation of innermost stable circular orbit(ISCO), margi…
In this paper, we construct thin-shell wormholes from regular Ayon-Beato and Garcia black hole by employing cut and paste formalism and examine their stability. We analyze attractive and repulsive characteristics of wormholes corresponding to outward and inward-directed acceleration components, respectively. A general equation of state is assumed as a linear perturbation to explore stability of these constructed wormholes with and without cosmological constant. We consider linear, logarithmic and Chaplygin gas models for exotic matter and evaluate stability regions for different values of char…
We study scalar, electromagnetic and gravitational test fields in the Hayward, Bardeen and Ayón-Beato-García regular black hole spacetimes and demonstrate that the test fields are stable in all these spacetimes. Using the sixth order WKB approximation of the linear "axial" perturbative scheme, we determine dependence of the quasinormal mode (QNM) frequencies on the characteristic parameters of the test fields and the spacetime charge parameters of the regular black holes. We give also the greybody factors, namely the transmission and reflection coefficients of scattered scalar, electromagnetic…
We analyze Bose-Einstein condensates on three types of spherically symmetric and static charged black-hole spacetimes: The Reissner-Nordström spacetime, Hoffmann's Born-Infeld black-hole spacetime, and the regular Ayón-Beato-García spacetime. The Bose-Einstein condensate is modeled in terms of a massive scalar field that satisfies a Klein-Gordon equation with a self-interaction term. The scalar field is assumed to be uncharged and not self-gravitating. If the mass parameter of the scalar field is chosen sufficiently small, there are quasi-bound states of the scalar field that may be interprete…
The present paper is aimed to study thermodynamical properties of phase transition for regular charged black holes. In this context, we have considered two different forms of black hole metrics supplemented with exponential and logistic distribution functions and investigated the recent expansion of phase transition through grand canonical ensemble. After exploring the corresponding Ehrenfest's equation, we found the second order background of phase transition at critical points. In order to check the critical behavior of regular black holes, we have evaluated some corresponding explicit relat…
We study the geodesics of charged black holes in polynomial Maxwell Lagrangians, a subclass of models within the nonlinear electrodynamics (NLED). Specifically, we consider black holes in Kruglov, power-law, and Ayon-Beato-Garcia models. Our exploration on the corresponding null bound states reveals that photon can orbit the extremal black holes in stable radii outside the corresponding horizon. The reason behind this is the well-known theorem that a photon in a NLED background propagates along its own {\it effective} geometry. This nonlinearity is able to shift the local minimum of the effect…
We study the shadows cast by the different types of rotating regular black holes viz. Ayón-Beato-García {(ABG)}, Hayward, and Bardeen. These black holes have in addition to the total mass ($M$) and rotation parameter ($a$), different parameters as electric charge ($Q$), deviation parameter ($g$), and magnetic charge ($g_{*}$), respectively. Interestingly, the size of the shadow is affected by these parameters in addition to the rotation parameter. We found that the radius of the shadow in each case decreases monotonically and the distortion parameter increases when the value of these parameter…
We drop the complexification procedure from the Newman-Janis algorithm and introduce more physical arguments and symmetry properties, and we show how one can generate regular and singular rotating black hole and non-black-hole solutions in Boyer-Lindquist coordinates. We focus on generic rotating regular black holes and show that they are regular on the Kerr-like ring but physical entities are undefined there. We show that rotating regular black holes have much smaller electric charges, and, with increasing charge, they turn into regular non-black-hole solutions well before their Kerr-Newman c…
We study the motion of a spinning particle with gravimagnetic moment in Schwarzschild-like spacetimes with a metric $ds^2=-f(r) dt^2 + f^{-1}(r) dr^2 + r^2 dΩ^2$, specifically we deal with Schwarzschild, Reissner-Nordstrom black holes as well as Ayon-Beato-Garcia and Bardeen regular spacetimes. First, we introduce the Hamiltonian system of equations which describes such kind of particles. In the case of null gravimagnetic moment, the equations are equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. Working in the equatorial plane, using the constants of motion generated by…
We obtain the mass parameter for a class of static and spherically symmetric regular black holes (BHs) (namely Bardeen, Hayward and Ayón-Beato-García BHs) which are solutions of Einstein's field equations coupled to nonlinear electrodynamics (NED) in terms of redshifts and blueshifts of photons emitted by geodesic particles (for instance, stars) orbiting around these BHs. The motion of photons is not governed by null geodesics for these type of spacetime geometries which reflects the direct effects of the electrodynamic nonlinearities in the photon motion; hence, an effective geometry needs to…
