Fadeev-Popov Ghosts and 1+1 Dimensional Black Hole Evaporation

TL;DR

This paper investigates how modifications from the Fadeev-Popov determinant affect two-dimensional black hole models, revealing non-singular solutions and novel interior geometries for certain matter field numbers.

Contribution

It introduces a modified set of semiclassical equations incorporating Fadeev-Popov effects, showing significant changes in black hole behavior for N<24, including non-singular shock wave solutions and deSitter interiors.

Findings

For N<24, equations become non-singular and complex singularities are avoided.

Shock waves reach null infinity with zero energy, cloaked by Hawking radiation.

Interior of black holes can be non-singular and asymptotically deSitter for small mass.

Abstract

Recently Callan, Giddings, Harvey and the author derived a set of one-loop semiclassical equations describing black hole formation/evaporation in two-dimensional dilaton gravity conformally coupled to $N$ scalar fields. These equations were subsequently used to show that an incoming matter wave develops a black hole type singularity at a critical value $\phi_{cr}$ of the dilaton field. In this paper a modification to these equations arising from the Fadeev-Popov determinant is considered and shown to have dramatic effects for $N<24$, in which case $\phi_{cr}$ becomes complex. The $N<24$ equations are solved along the leading edge of an incoming matter shock wave and found to be non-singular. The shock wave arrives at future null infinity in a zero energy state, gravitationally cloaked by negative energy Hawking radiation. Static black hole solutions supported by a radiation bath are also studied. The interior of the event horizon is found to be non-singular and asymptotic to deSitter space for $N<24$, at least for sufficiently small mass. It is noted that the one-loop approximation is {\it not} justified by a small parameter for small $N$. However an alternate theory (with different matter content) is found for which the same equations arise to leading order in an adjustable small parameter.