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 parameter which will support pressure coordinate in the thermodynamic perspective of this black hole in our setup. We should be point that this formal variable cosmological parameter is different with cosmological constant which comes from AdS/CFT correspondence and it is effective at large distances as AdS space pressure. In our setup the assumed pressure is originated from internal material of the black hole say q and m here. By calculating the Hawking temperature of this black hole we obtain equation of state. Then we plotted isothermal P-v curves and heat capacity at constant pressure. They show that the system participates in the small to large phase transition of the black hole or the Hawking-Page phase transition which is similar to the Van der Waals phase transition in the ordinary thermodynamics systems . In fact in the Hawking-Page phase transition disequilibrium evaporating generalized ABG black hole reaches to a vacuum AdS space finally.
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…
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…
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 $α$, $λ$…
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…
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…
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 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…
We consider a higher derivative gravity theory in four dimensions with a negative cosmological constant and show that vacuum solutions of both Lifshitz type and Schrödinger type with arbitrary dynamical exponent z exist in this system. Then we find an analytic black hole solution which asymptotes to the vacuum Lifshitz solution with z=3/2 at a specific value of the coupling constant. We analyze the thermodynamic behavior of this black hole and find that the black hole has zero entropy while non-zero temperature, which is very similar to the case of BTZ black holes in new massive gravity at a s…
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…
