Four-dimensional black holes in Einsteinian cubic gravity

TL;DR

This paper constructs and analyzes new four-dimensional black hole solutions in Einsteinian cubic gravity, demonstrating their thermodynamic properties and stability, and establishing ECG as the most general such theory up to cubic order.

Contribution

It provides the first explicit construction of static, spherically symmetric black holes in 4D Einsteinian cubic gravity with analytical thermodynamic quantities.

Findings

Solutions satisfy the first law of black-hole mechanics.

Some solutions exhibit positive specific heat, indicating thermodynamic stability.

ECG is the most general 4D gravity theory with non-trivial black hole solutions up to cubic curvature terms.

Abstract

We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordstr\"om-(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.