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.
Highlights
General relativity (GR) describes accurately the dynamics of the gravitational field in the regime of relatively low curvature, but modifications of this theory are expected to appear at high energies
We show that the AdS2 × S2 near-horizon geometry of Reissner-Nordström 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 find additional solutions that do not reduce to AdS2 × S2 geometries in any limit and that do not have a counterpart in Einstein gravity
Summary
General relativity (GR) describes accurately the dynamics of the gravitational field in the regime of relatively low curvature, but modifications of this theory are expected to appear at high energies. Known as generalized quasitopological gravities (GQTGs) [32], these theories allow for simple spherically symmetric black hole solutions whose thermodynamic properties can be studied. We will show in this paper that the equations of motion of ECG reduce in this case to a single second-order ordinary differential equation (ODE) This equation has to be solved numerically, but most remarkably, we will see that it is possible to obtain the exact expressions for the area and entropy of these black holes without using any approximation. We will add as well a Maxwell field into the game, which will allow us to study rotating and charged extremal black holes This will prove to be useful, as AdS2 × S2 geometries—corresponding to nonrotating charged black holes—are always solutions of higher-order gravities.
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