# On black holes in higher-derivative gravities

## TL;DR

This paper investigates static, spherically symmetric black hole solutions in higher-derivative gravity theories, establishing criteria for their existence, uniqueness, and thermodynamic properties, and providing new solutions in specific models.

## Contribution

It identifies conditions under which higher-derivative gravities admit simple, mass-determined black hole solutions and offers a systematic method for constructing and analyzing them.

## Key findings

- Only theories with a massless, traceless graviton admit certain black hole solutions.
- Provided a sufficient condition for the existence of these solutions.
- Constructed new black hole solutions in generalized quasitopological gravity.

## Abstract

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), and 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 [arXiv:1703.01631], which belongs to the class of theories selected by our results.