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(tt)g(rr) - -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.