Magnetically charged regular black hole in a model of nonlinear electrodynamics

Abstract

We obtain a magnetically charged regular black hole in general relativity. The source to the Einstein field equations is nonlinear electrodynamic field in a physically reasonable model of nonlinear electrodynamics (NED). "Physically" here means the NED model is constructed on the basis of three conditions: the Maxwell asymptotic in the weak electromagnetic field limit; the presence of vacuum birefringence phenomenon; and satisfying the weak energy condition (WEC). In addition, we analyze the thermodynamic properties of the regular black hole in two ways. According to the usual black hole thermodynamics, we calculate the heat capacity at constant charge, from which we know the smaller black hole is more stable. We also employ the horizon thermodynamics to discuss the thermodynamic quantities, especially the heat capacity at constant pressure. PACS numbers: 04.70.Dy I. INTRODUCTION The first well-known model of nonlinear electrodynamics(NED) is the Born-Infeld theory(BI), which is proposed to obtain a finite electron self-energy[1]. Heisenberg and Euler found that due to the presence of virtual charged particles the one-loop quantum correction in quantum electrodynamics will give nonlinear contribution[2]. Not only that, the virtual particles will result in " polarization of the vacuum ". In this case, the vacuum behaves like a polarizable continuum and should exhibit the phenomenon of birefringence[3-5]. These effects can be observed in experiments such as PVLAS[6] and BMV[7] and the experimental results can put some restrictions on the parameters introduced in the NED models. Vacuum birefringence is a nonlinear effect. Therefore, we expect that in a physically reasonable model of NED, there should exist the effect of vacuum birefringence. In this sense, the usual BI theory is not a physically allowable NED model because of the absence of vacuum birefringence. However, in the generalized BI model with two parameters the vacuum birefringence may exist[8]. The nonlinear effects in electrodynamics are significant only *

Construction of regular black holes in general relativity

“…For M = 0 , µ = 3, the solution is the Hayward black hole [9] which has been constructed in [22]. For the solution with zero Schwarzschild mass, the behavior of the metric function f and the low lying curvature polynomials are still given by (19) and (20) respectively. Thus, the regular black hole solution has µ ≥ 3 as well.…”

Dyonic configurations in nonlinear electrodynamics coupled to general relativity

“…Thermodynamic properties of regular NED BHs were discussed in [17,18,19,21,20,22,23,24], in particular, the first law of thermodynamics, heat capacity, the validity of Smarr's formula for the BH mass, etc.…”

“…Many authors studied the stability properties of NED BHs [32,33,34,35,36,20] and their quasinormal modes related to different kinds of perturbations [37,35,36,38,16] in cases where these BHs are stable. In particular, simple conditions on the NED Lagrangian have been derived, which imply linear stability in the domain of outer communication [32], and linear stability has been verified for a number of particular examples.…”

Exact black hole solutions with nonlinear electrodynamic field

“…It is found that not only the Big-Bang singularity but also the black hole singularity can be avoided by using the non-linear electromagnetic field. Correspondingly, some regular black hole solutions without singularities are obtained [59][60][61][62][63][64][65][66][67][68][69][70]. As for the black hole horizons, the Kerr-Newman-de Sitter spacetime has at most three horizons, the inner horizon, the event horizon and the cosmic horizon.…”