Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# 4D Einstein-Gauss-Bonnet Gravity Coupled with Nonlinear Electrodynamics

Version 1 : Received: 1 December 2020 / Approved: 2 December 2020 / Online: 2 December 2020 (08:05:42 CET)

A peer-reviewed article of this Preprint also exists.

Kruglov, S.I. 4D Einstein–Gauss–Bonnet Gravity Coupled with Nonlinear Electrodynamics. Symmetry 2021, 13, 204. Kruglov, S.I. 4D Einstein–Gauss–Bonnet Gravity Coupled with Nonlinear Electrodynamics. Symmetry 2021, 13, 204.

Journal reference: Symmetry 2021, 13, 204
DOI: 10.3390/sym13020204

## Abstract

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ 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 radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

## Subject Areas

Einstein-Gauss-Bonnet gravity; nonlinear electrodynamics; Hawking temperature; heat capacity; black hole shadow

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