Radiating black holes in Einstein-Maxwell-dilaton theory and cosmic censorship violation

TL;DR

This paper constructs exact dynamical black hole solutions in Einstein-Maxwell-dilaton theory, revealing that for a specific coupling, black holes can be overcharged to form naked singularities, thus violating cosmic censorship.

Contribution

It provides the first exact, time-dependent solutions in Einstein-Maxwell-dilaton theory with arbitrary coupling and demonstrates cosmic censorship violation for the special case of coupling a=1.

Findings

For a=1, black holes can be overcharged to form naked singularities.

Solutions generalize Vaidya and Bonnor-Vaidya solutions to Einstein-Maxwell-dilaton theory.

Time-dependent dilaton field exists only at a=1 in these solutions.

Abstract

We construct exact, time-dependent, black hole solutions of Einstein-Maxwell-dilaton theory with arbitrary dilaton coupling, $a$. For $a=1$ this theory arises as the four-dimensional low-energy effective description of heterotic string theory. These solutions represent electrically charged, spherically symmetric black holes emitting or absorbing charged null fluids and generalize the Vaidya and Bonnor-Vaidya solutions of general relativity and of Einstein-Maxwell theory, respectively. The $a=1$ case stands out as special, in the sense that it is the only choice of the coupling that allows for a time-dependent dilaton field in this class of solutions. As a by-product, when $a=1$ we show that an electrically charged black hole in this theory can be overcharged by bombarding it with a stream of electrically charged null fluid, resulting in the formation of a naked singularity. This provides an example of cosmic censorship violation in an exact dynamical solution to low-energy effective string theory and in a case in which the total stress-energy tensor satisfies all energy conditions. When $a\neq1$, our solutions necessarily have a time-independent scalar field and consequently cannot be overcharged.