Two-dimensional black hole in the three-dimensional black string.

Abstract

We discuss the two-dimensional black hole in the (2+1)-dimensional black string. When the charge of the black string Q=0 and thus the torsion ${\mathit{H}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}\mathrm{\ensuremath{\rho}}}$ vanishes, a black string with double horizons becomes a simple product of a two-dimensional (2D) black hole with a single horizon and R. It is shown that the two propagating modes are the dilaton and tachyon in a 3D black string background, and L=h-\ensuremath{\varphi} and the tachyon in a 2D black hole \ensuremath{\bigotimes}R background. We also calculate the reflection and transmission coefficients for the scattering of string fields off 2D black holes. Using the Bogoliubov transformation we find the Hawking temperature from the reflection coefficient of the tachyon.