Nonsingular Black Holes in 4D Einstein–Gauss–Bonnet Gravity

Abstract

Recently, several methods have been proposed to regularize a D→4 limit of Einstein–Gauss–Bonnet (EGB), leading to nontrivial gravitational dynamics in 4D. We present an exact nonsingular black hole solution in the 4D EGB gravity coupled to non-linear electrodynamics and analyze their thermodynamic properties to calculate precise expressions for the black hole mass, temperature, and entropy. Because of the magnetic charge, the thermodynamic quantities are corrected, and the Hawking–Page phase transition is achievable with diverges of the heat capacity at a larger critical radius r=r+C in comparison to the 5D counterpart where the temperature is maximum. Thus, we have a black hole with Cauchy and event horizons, and its evaporation leads to a thermodynamically stable extremal black hole remnant with vanishing temperature, and its size is larger than the 5D counterpart. The entropy does not satisfy the usual exact horizon Bekenstein–Hawking area law of general relativity with a logarithmic area correction term.

Nonsingular black hole chemistry in $4D$ Einstein-Gauss-Bonnet gravity

“…Here, A = 4πr 2 + is the black hole event horizon area, and A 0 is a constant with the area units. This equation generalizes the Hawking-Bekenstein area formula [79] by a supplementary logarithmic term and third in the above expression is due to magnetic charge g. Notice that, in limit α → 0, we obtain the entropy of the Hayward black hole [24]. Here, it is interesting to note that entropy of nonsingular-AdS EGB black holes does not depend explicitly on the pressure P of the system, but the horizon radius r + of the black hole depends on pressure P ; hence the pressure of the black hole affects its entropy.…”

“…is the Lagrangian density of the NED, which for the nonsingular black hole solutions we are interested in, is given as [24,55]…”

“…Here, we want to obtain the static spherically symmetric black hole solutions of Eq. ( 1), hence we consider the following metric [24,55]…”

“…Nevertheless, several researchers attracted to analyse this 4D EGB theory, in particular, the spherically symmetric black hole solution obtained by Glavan and Lin [17] was extended to include charge [20], a nonstatic Vaidya-like radiating black hole in Ref. [21,22], black holes coupled with NED [23][24][25], with cloud of string background [26]. The black hole stability and quasinormal modes are also widely discussed [27][28][29][30][31][32], and the rotating counter of the black holes obtained [33,34].…”

The shadow of regular black holes with asymptotically Minkowski core

“…Recently, the investigation on the shadows has been extended to regular black holes as well, including rotating Bardeen and Hayward black holes [23][24][25][26]. In history, regular black holes are proposed to resolve the singularity problem in classical general relativity.…”