Radiating Black Holes in General Relativity Need Not Be Singular

It is common knowledge that black holes necessarily contain a region where general relativity breaks down, due to the inevitable formation of either a curvature singularity or a Cauchy horizon. In this Letter we challenge this view by analyzing a charged spherically symmetric black hole formed through gravitational collapse and evaporating via Hawking radiation. We show that the electromagnetic repulsion and the violation of energy conditions due to the presence of Hawking radiation can be sufficient to avoid the formation of both a singularity and a Cauchy horizon. We argue that a similar mechanism may apply to astrophysical black holes in which the role of the electric charge is replaced by the angular momentum.