Radiating black holes in general relativity need not be singular

Abstract

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 work 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 are 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.

Figures (3)

• Figure 1: Gravitational collapse into a Schwarzschild black hole.
• Figure 2: Gravitational collapse leading to the formation of a Reissner--Nordstrom black hole. In the left diagram, the radiation matter forming the black hole collapses into one single point forming a timelike singularity. In the right diagram, matter bounces inside the trapping horizon and crosses a Cauchy horizon.
• Figure 3: Different possible scenarios for the end-point of the gravitational collapse. In the top left diagram, the trapped region evaporates in finite time leaving a remnant. In the top right diagram, the trapped region evaporate in finite time leaving no remnant. In the bottom left region the trapped region evaporates in infinite time leaving no remnant. Finally, in the bottom right region, the trapped region evaporates in infinite time leaving a remnant. Only the last scenario implies a breakdown of predictability, while the other cases lead to a regular spacetime with no Cauchy horizon.