Lamb Shift for static atoms outside a Schwarzschild black hole

TL;DR

This paper investigates the Lamb shift of a static atom near a Schwarzschild black hole, revealing how different vacuum states influence the shift through backscattering and thermal effects.

Contribution

It provides a detailed analysis of the Lamb shift in various black hole vacuum states, highlighting the effects of backscattering and thermal radiation on atomic energy levels.

Findings

Lamb shift in Boulware vacuum is affected by backscattering off space-time curvature.

In Unruh and Hartle-Hawking vacua, the shift mimics thermal radiation effects.

Thermal radiation is backscattered by the black hole geometry.

Abstract

We study, by separately calculating the contributions of vacuum fluctuations and radiation reaction to the atomic energy level shift, the Lamb shift of a static two-level atom interacting with real massless scalar fields in the Boulware, Unruh and Hartle-Hawking vacuums outside a Schwarzschild black hole. We find that in the Boulware vacuum, the Lamb shift gets a correction arising as a result of the backscattering of vacuum field modes off the space-time curvature, which is reminiscent of the correction to the Lamb shift induced by the presence of cavities. However, when the Unruh and Hartle-Hawking vacua are concerned, our results show that the Lamb shift behaves as if the atom were irradiated by a thermal radiation or immersed in a thermal bath at the Hawking temperature, depending on whether the scalar field is in the Unruh or the Hartle-Hawking vacuum. Remarkably, the thermal radiation is always backscattered by the space-time geometry.