On black holes in higher-derivative gravities

We establish various general results concerning static and spherically symmetric black hole solutions of general higher-derivative extensions of Einstein gravity. We prove that the only theories susceptible of admitting solutions with g t t g r r = − 1 and representing the exterior field of a spherically symmetric distribution of mass are those that only propagate a massless and traceless graviton on the vacuum. Then, we provide a simple—and computationally powerful—sufficient condition for a theory to admit solutions of that kind, as well as a systematic way for constructing them for a given theory. We conjecture (and provide strong evidence) that all black holes constructed according to our criteria are completely determined by their mass (non-hairy), such that their thermodynamic properties can be obtained by solving a system of algebraic equations without free parameters. Our results can be straightforwardly extended to planar and hyperbolic horizons. We illustrate this by obtaining new planar asymptotically AdS 5 black hole solutions of the recently constructed generalized quasitopological gravity (Hennigar et al Phys. Rev . D 95 104042), which belongs to the class of theories selected by our results.