Interaction of the gravitational Hawking radiation and a static point mass

TL;DR

This paper analyzes how a static point mass near a Schwarzschild black hole interacts with Hawking radiation gravitons, deriving finite response rates and comparing black hole and Rindler spacetime effects.

Contribution

It provides a closed-form expression for the response rate of a static point mass to Hawking gravitons and compares it with Rindler spacetime, revealing the black hole size as an infrared cutoff.

Findings

Response rate is finite near the black hole horizon.

Black hole size acts as an infrared cutoff.

Response rate vanishes in the Hartle-Hawking state.

Abstract

We study the interaction of a stress-energy tensor describing a static point mass supported by a string outside a Schwarzschild black hole with the gravitons of the Hawking radiation. We derive a closed-form analytic expression for the total response rate of this stress-energy tensor to the thermal gravitons in the Unruh state, which models the quantum state in the spacetime of a spherically symmetric black hole formed by gravitational collapse. This response rate is finite in contrast with the infrared divergent response rate for a static point mass supported by a string in Rindler spacetime, i.e., a point mass accelerated uniformly by a string in Minkowski spacetime. By comparing the response rate near the black hole horizon with that in Rindler spacetime, we show that the size of the black hole acts as a natural infrared cutoff. We also find that the response rate of this stress-energy tensor to the thermal gravitons incoming from past null infinity in the Hartle-Hawking state vanishes. As a result, the total response rate of a static point mass (supported by a string) in the Unruh and Hartle-Hawking states for gravitons are identical. This is also the case for a static charge interacting with the electromagnetic field but not for a static source for a massless scalar field.