The Quantum Stress Tensor in the Three Dimensional Black Hole

TL;DR

This paper calculates the quantum stress tensor in a 2+1 dimensional black hole, revealing its behavior at horizons and singularities, and suggesting inner horizon instability due to quantum effects.

Contribution

It provides the first explicit calculation of the quantum stress tensor in the BTZ black hole using the method of images.

Findings

Stress tensor is finite at the event horizon for non-rotating black holes.

Stress tensor diverges at the singularity.

Inner horizon shows divergence, indicating potential quantum instability.

Abstract

The quantum stress tensor $<T_{\mu\nu}>$ is calculated in the 2+1 dimensional black hole found by Banados, Teitelboim, and Zanelli. The Greens function, from which $<T_{\mu\nu}> $ is derived, is obtained by the method of images. For the non-rotating black hole, it is shown that $<T_{\mu\nu}>$ 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.