Do static atoms outside a Schwarzschild black hole spontaneously excite?

TL;DR

This paper investigates how a static atom outside a Schwarzschild black hole interacts with a scalar field in different vacua, revealing conditions under which it spontaneously excites or remains stable.

Contribution

It provides a detailed analysis of spontaneous excitation phenomena for atoms near black holes in various quantum vacuum states, highlighting differences from flat spacetime.

Findings

Atoms are stable in Boulware vacuum.

Atoms spontaneously excite in Unruh and Hartle-Hawking vacua.

Excitation resembles thermal radiation at Hawking temperature.

Abstract

The spontaneous excitation of a two-level atom held static outside a four dimensional Schwarzschild black hole and in interaction with a massless scalar field in the Boulware, Unruh and Hartle-Hawking vacuum is investigated and the contributions of the vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy are calculated separately. We find that for the Boulware vacuum, the spontaneous excitation does not occur and the ground state atoms are stable, while the spontaneous emission rate for excited atoms in the Boulware vacuum, which is well-behaved at the event horizon, is not the same as that in the usual Minkowski vacuum. However, both for the Unruh vacuum and the Hartle-Hawking vacuum, our results show that the atom would spontaneously excite, as if there were an outgoing thermal flux of radiation or as if it were in a thermal bath of radiation at a proper temperature which reduces to the Hawking temperature in the spatial asymptotic region, depending on whether the scalar field is in the Unruh or Hartle-Hawking vacuum.