Stress-Energy Tensor for the Massless Spin 1/2 Field in Static Black Hole Spacetimes

TL;DR

This paper numerically computes the stress-energy tensor for a massless spin 1/2 field around various static black holes, revealing discrepancies with previous analytic approximations and clarifying the behavior near horizons.

Contribution

It provides the first numerical analysis of the stress-energy tensor for massless spin 1/2 fields in static black hole spacetimes, challenging existing analytic predictions.

Findings

Stress-energy tensor differs in sign from analytic approximations for Schwarzschild black holes.

No divergences occur at horizons in Reissner-Nordstrom solutions as previously predicted.

Numerical results show significant deviations from analytic models near black hole horizons.

Abstract

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static non-rotating black holes, corresponding to the Schwarzschild, Reissner-Nordstrom and extreme Reissner-Nordstr\"om solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress-energy differs even in sign from the analytic approximation. For the Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences predicted by the analytic approximations are shown not to exist.