Geometric phase outside a Schwarzschild black hole and the Hawking effect

TL;DR

This paper investigates how the geometric phase of a two-level atom outside a Schwarzschild black hole is influenced by Hawking radiation, suggesting geometric phase measurements could detect black hole radiation effects.

Contribution

It introduces a novel approach linking geometric phase shifts to Hawking radiation, analyzing effects in different vacua around a black hole.

Findings

Geometric phase is affected by space-time curvature and vacuum state.

In Unruh and Hartle-Hawking vacua, phase behaves as if thermal radiation at Hawking temperature.

Measurement of phase change can reveal Hawking radiation presence.

Abstract

We study the Hawking effect in terms of the geometric phase acquired by a two-level atom as a result of coupling to vacuum fluctuations outside a Schwarzschild black hole in a gedanken experiment. We treat the atom in interaction with a bath of fluctuating quantized massless scalar fields as an open quantum system, whose dynamics is governed by a master equation obtained by tracing over the field degrees of freedom. The nonunitary effects of this system are examined by analyzing the geometric phase for the Boulware, Unruh and Hartle-Hawking vacua respectively. We find, for all the three cases, that the geometric phase of the atom turns out to be affected by the space-time curvature which backscatters the vacuum field modes. In both the Unruh and Hartle-Hawking vacua, the geometric phase exhibits similar behaviors as if there were thermal radiation at the Hawking temperature from the black hole. So, a measurement of the change of the geometric phase as opposed to that in a flat space-time can in principle reveal the existence of the Hawking radiation.