Extremal Rotating Black Holes in Einsteinian Cubic Gravity

TL;DR

This paper derives new extremal rotating black hole solutions in Einsteinian cubic gravity, revealing corrections to known geometries, and provides exact entropy formulas, advancing understanding of higher-order gravity black holes.

Contribution

It presents the first exact entropy calculation for rotating black holes in higher-order gravity and constructs novel solutions with no Einstein gravity counterparts.

Findings

Reissner-Nordström near-horizon geometry remains uncorrected.

Deviations from Kerr-Newman appear with angular momentum.

Exact expressions for black hole entropy are obtained.

Abstract

We obtain new solutions of Einsteinian cubic gravity coupled to a Maxwell field that describe the near-horizon geometry of charged and rotating black holes. We show that the AdS$_2\times\mathbb{S}^2$ near-horizon geometry of Reissner-Nordstr\"om black holes receives no corrections, but deviations with respect to the extremal Kerr-Newman solution appear as we turn on the angular momentum. We construct the profile of these corrected geometries using both numerical methods and slowly-spinning expansions, but we also find additional solutions that do not reduce to AdS$_2\times\mathbb{S}^2$ geometries in any limit and that do not have a counterpart in Einstein gravity. Quite remarkably, we are able to obtain closed-form exact expressions for the area and Wald's entropy of all of these solutions, and using this result, we analyze the phase space of extremal back holes in this theory. To the best of our knowledge, this is the first time the entropy of a rotating black hole in higher-order gravity has been exactly computed.