Spherically symmetric black holes in metric gravity

The existence of black holes is one of the key predictions of general relativity (GR) and therefore one of the basic consistency tests for modified theories of gravity. In spherical symmetry GR admits only two distinct classes of physical black holes. Assuming only the existence of an apparent horizon and its regularity, we derive constraints that any self-consistent modified theory of gravity must satisfy to be compatible with their existence. We analyze their properties and illustrate characteristic features using the Starobinsky model. Only one of the two possible solutions of GR can be regarded as zeroth-order perturbative solution of this model. On the other hand, we show that it is possible to construct non-perturbative solutions without a well-defined GR limit.