Four-dimensional black holes in Einsteinian cubic gravity

Abstract

We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordström-(Anti-)de Sitter (RN-(A)dS) black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are determined by a single blackening factor which satisfies a non-linear second-order differential equation. Interestingly, we are able to compute independently the Hawking temperature $T$, the Wald entropy $\mathsf{S}$ and the Abbott-Deser mass $M$ of the solutions analytically as functions of the horizon radius and the ECG coupling constant $\lambda$. Using these we show that the first law of black-hole mechanics is exactly satisfied. Some of the solutions have positive specific heat, which makes them thermodynamically stable, even in the uncharged and asymptotically flat case. Further, we claim that, up to cubic order in curvature, ECG is the most general four-dimensional theory of gravity which allows for non-trivial single-blackening factor generalizations of Schwarzschild- and RN-(A)dS which reduce to the usual Einstein gravity solutions when the corresponding higher-order couplings are set to zero.

13 pp, 5 figs; v3: minor modifications to match published version

References in corpus (5)

• Black Holes in Higher-Derivative Gravity
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Einsteinian cubic gravity
• AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities
• Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions

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• Horndeski Gravity and the Violation of Reverse Isoperimetric Inequality
• Higher order gravities and the Strong Equivalence Principle
• Termodinámica de agujeros negros y campos escalares