Semiclassical Stability of the Extreme Reissner-Nordstrom Black Hole

TL;DR

This paper investigates the quantum stability of the extreme Reissner-Nordstrom black hole by calculating the stress-energy tensor of a scalar field, showing regularity at the horizon for the vacuum state but divergence at nonzero temperatures.

Contribution

It provides an analytic calculation of the stress-energy tensor in the black hole spacetime, demonstrating stability in the zero-temperature vacuum state.

Findings

Stress-energy tensor is regular at the horizon in the vacuum state.

Stress-energy diverges at the horizon for nonzero temperature states.

Contradicts previous two-dimensional calculations suggesting divergence.

Abstract

The stress-energy tensor of a free quantized scalar field is calculated in the extreme Reissner-Nordstr\"{o}m black hole spacetime in the zero temperature vacuum state. The stress-energy appears to be regular on the event horizon, contrary to the suggestion provided by two-dimensional calculations. An analytic calculation on the event horizon for a thermal state shows that if the temperature is nonzero then the stress-energy diverges strongly there.