Electromagnetic quasitopological gravities
Abstract
We identify a set of higherderivative extensions of EinsteinMaxwell 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 nonminimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magneticallycharged 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 higherderivative 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 Noethercharge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal chargetomass ratio at a nonperturbative 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2020
 DOI:
 10.1007/JHEP10(2020)125
 arXiv:
 arXiv:2007.04331
 Bibcode:
 2020JHEP...10..125C
 Keywords:

 Black Holes;
 Classical Theories of Gravity;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 56 pages, 6 figures. Matches version published in JHEP. New appendix added explaining the validity of the reduced Lagrangian method to obtain the equations of motion