Quantum stress tensor in the three-dimensional black hole

Abstract

The quantum stress tensor 〈${\mathit{T}}_{\mathrm{\mu }\nu }$〉 is calculated in the (2+1)-dimensional black hole found by Banados, Teitelboim, and Zanelli. The Green’s function, from which 〈${\mathit{T}}_{\mathrm{\mu }\nu }$〉 is derived, is obtained by the method of images. For the nonrotating black hole, it is shown that 〈${\mathit{T}}_{\mathrm{\mu }\nu }$〉 is finite on the event horizon, but diverges at the singularity. For the rotating solution, the stress tensor is finite at the outer horizon, but diverges near the inner horizon. This suggests that the inner horizon is quantum mechanically unstable against the formation of a singularity.