Liouville Models of Black Hole Evaporation

TL;DR

This paper develops new two-dimensional dilaton gravity models coupled with conformal matter, allowing exact solutions for black hole evaporation scenarios, and discusses potential issues with Hawking radiation in these models.

Contribution

It introduces new $c=26$ conformal field theory-based models of dilaton gravity that differ from previous models and are exactly solvable, enabling detailed analysis of black hole dynamics.

Findings

Exact classical solutions for static and dynamic cases.

Identification of unphysical negative Hawking radiation in some solutions.

Discussion on resolving quantum-level issues with Hawking radiation.

Abstract

We construct new theories of dilation gravity coupled to conformal matter which are exact $c=26$ conformal field theories and presumably consistent frameworks for discussing black hole physics in two dimensions. They differ from the CGHS equations in the precise dilaton dependence of the cosmological constant. A further modification proposed by Strominger with a view to eliminating unphysical ghost Hawking radiation is also considered. The new classical equations of motion are explicitly soluble, thus permitting an exact analysis of both static and dynamic senarios. While the static solutions are physically reasonable, the dynamical solutions include puzzling examples with wrong-sign Hawking radiation. We indicate how the latter problem may be resolved in the full quantum theory.