The Lamb shift in the BTZ spacetime

TL;DR

This paper investigates the Lamb shift of a two-level atom in BTZ spacetime, revealing how it is influenced by the spacetime's geometry and proximity to the horizon, with results comparable to flat spacetime scenarios.

Contribution

It provides a detailed analysis of the Lamb shift in BTZ spacetime, highlighting the effects of the spacetime's structure and boundary conditions on atomic energy level shifts.

Findings

Lamb shift is suppressed compared to flat spacetime when transition wavelength exceeds AdS radius.

Lamb shift can be suppressed or enhanced when transition wavelength is less than AdS radius.

Near the horizon, the Lamb shift is suppressed and approaches flat spacetime values despite diverging temperature.

Abstract

We study the Lamb shift of a two-level atom arising from its coupling to the conformal massless scalar field, which satisfies the Dirichlet boundary conditions, in the Hartle-Hawking vacuum in the BTZ spacetime, and find that the Lamb shift in the BTZ spacetime is structurally similar to that of a uniformly accelerated atom near a perfectly reflecting boundary in (2+1)-dimensional flat spacetime. Our results show that the Lamb shift is suppressed in the BTZ spacetime as compared to that in the flat spacetime as long as the transition wavelength of the atom is much larger than $AdS$ radius of the BTZ spacetime while it can be either suppressed or enhanced if the transition wavelength of the atom is much less than $AdS$ radius. In contrast, the Lamb shift is always suppressed very close to the horizon of the BTZ spacetime and remarkably it reduces to that in the flat spacetime as the horizon is approached although the local temperature blows up there.