Semi-classical Approach to Charged Dilatonic Black Hole in Two Dimensions

TL;DR

This paper develops an exactly solvable semi-classical model of two-dimensional charged dilatonic black holes, revealing conditions under which singularities are cloaked or disappear, and indicating possible topology change during collapse.

Contribution

It introduces a semi-classical framework with quantum corrections for charged dilatonic black holes, analyzing singularity behavior and topology change in different parameter regimes.

Findings

Quantum corrections can cloak or eliminate singularities.

Discontinuities in the metric suggest topology change.

Certain parameter regimes lead to naked singularities or their absence.

Abstract

We consider exactly solvable semi-classical theory of two dimensional dilatonic gravity with electromagnetic interactions. As was done in the paper by Russo, Susskind and Thorlacius, the term which changes the kinetic term is added to the action. The theory contains massless fermions as matter fields and there appear the quantum corrections including chiral anomaly. The screening effect due to the chiral anomaly has a tendency to cloak the singularity. In a region of the parameter space, the essential behavior of the theory is similar to that of Callan, Giddings, Harvey and Strominger's dilatonic black hole theory modified in the paper by Russo, Susskind and Thorlacius and the singularity formed by the collapsing matter emerges naked. We find, however, another region of the parameter space where the singularity disappears in a finite proper time. Furthermore, in the region of the parameter space, there appears a discontinuity in the metric on the trajectory of the collapsing matter, which would be a signal of topology change