Three-Dimensional Black Holes and String Theory

TL;DR

This work computes the exact decay rate for a massless scalar in the 2+1D BTZ black hole by solving the wave equation analytically and matching ingoing/outgoing fluxes. The radial equation is reduced to a hypergeometric form, yielding an exact absorption cross section in terms of Gamma functions. In the low-energy, zero-angular-momentum limit, the semiclassical decay rate coincides with a two-sector conformal field theory prediction, expressed via left and right temperatures, thereby reinforcing the effective string description in 3D. The results extend the AdS3/CFT correspondence to non-extremal BTZ black holes and connect to exact SL(2,R) WZW string theory realizations of the background.

Abstract

The exact decay rate for emission of massless minimally coupled scalar fields by a non-extremal black hole in 2+1 dimensions is obtained. At low energy, the decay rate into scalars with zero angular momentum is correctly reproduced within conformal field theory. The conformal field theory has both left- and right-moving sectors and their contribution to the decay rate is associated naturally with left and right temperatures of the black hole.