Electromagnetic Quasitopological Gravities

TL;DR

This paper introduces higher-derivative extensions of Einstein-Maxwell theory that admit analytic, regular charged black hole solutions, preserving thermodynamic laws and revealing novel extremal black hole properties with implications for black hole evaporation.

Contribution

It constructs a new class of non-minimally coupled quasitopological gravities with analytic solutions and explores their black hole thermodynamics and extremal properties.

Findings

Regular black hole solutions without singularities.

Exact thermodynamic relations for charged black holes.

Existence of extremal black holes with modified charge-to-mass ratios.

Abstract

We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function $f(r)=-g_{tt}=1/g_{rr}$. These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated, enabling us to obtain analytic solutions. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections and that the solution describes a globally regular geometry. In other cases, the equations are reduced to a second order equation for $f(r)$. Nevertheless, for all the theories it is possible to study the thermodynamic properties of charged black holes analytically. We show that the first law of thermodynamics holds exactly and that the Euclidean and Noether-charge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal charge-to-mass ratio at a non-perturbative level. We observe that in some theories there are no extremal black holes below certain mass. We also show the existence of theories for which extremal black holes do not represent the minimal mass state for a given charge. The implications of these findings for the evaporation process of black holes are discussed.