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

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.

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