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Global geometry of two-dimensional charged black holes

Andrei V. Frolov·Kristjan R. Kristjansson·Larus Thorlacius
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Abstract

The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes any extension of the spacetime geometry. At the classical level, a static solution describing an eternal black hole has timelike singularities and multiple asymptotic regions. The corresponding semiclassical solution, on the other hand, has a spacelike singularity and a Penrose diagram like that of an electrically neutral black hole. Extremal black holes are destabilized by pair-creation of charged particles. There is a maximally charged solution for a given black hole mass but the corresponding geometry is not extremal. Our numerical data exhibits critical behavior at the threshold for black hole formation.

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Andrei V. Frolov, Kristjan R. Kristjansson, Larus Thorlacius. 2006-04-12. Global geometry of two-dimensional charged black holes. https://doi.org/10.1103/physrevd.73.124036

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