Four-dimensional black holes in Einsteinian cubic gravity

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 characterized by a single function which satisfies a nonlinear 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 nontrivial generalizations of Schwarzschild- and RN-(A)dS characterized by a single function which reduce to the usual Einstein gravity solutions when the corresponding higher-order couplings are set to zero.