4D Einstein–Gauss–Bonnet Gravity Coupled with Nonlinear Electrodynamics

Sergey Il’Ich Kruglov

doi:10.3390/sym13020204

Abstract

A new exact spherically symmetric and magnetically charged black hole solution in regularization scheme of Glavan and Lin is obtained. The nonlinear electrodynamics Lagrangian is given by LNED=−F/(1+2βF4), where F is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radius is calculated and we study its dependance on model parameters.

Highlights

The heterotic string theory at the low energy limit gives models of gravity with higher order curvature terms in the action [1,2,3,4,5]
Glavan and Lin [6] shown that if the coupling constant α, which can be considered as the inverse of the string tension, is rescaled by α/( D − 4), in the limit D → 4, this scheme yields a non-trivial dynamics without singularities
It was shown that the BH can have two horizons or one extreme horizon, or not horizons corresponding to particle-like solution, depending on the model parameters

Summary

Introduction

The heterotic string theory at the low energy limit gives models of gravity with higher order curvature terms in the action [1,2,3,4,5]. Glavan and Lin [6] shown that if the coupling constant α, which can be considered as the inverse of the string tension, is rescaled by α/( D − 4), in the limit D → 4, this scheme yields a non-trivial dynamics without singularities It was argued, that the model being a classical modified gravity, is free from the Ostrogradsky instability and conserves the number of degrees of freedom. The static spherically symmetric BH solution for the Einstein GB gravity was obtained in [7,8,9] and the authors claimed that the GB term can be considered as a quantum correction to GR. The GR coupled with NED, having the Maxwell limit F → 0, does not admit a static, spherically symmetric solution with a regular center and a nonzero electric charge [47].

The BH Thermodynamics

The Black Hole Shadow

Conclusions