The Lamb shift in the BTZ spacetime

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.

21 pages,2 figures

References in corpus (9)

• Static, stationary and inertial Unruh-DeWitt detectors on the BTZ black hole
• Quantum Fluctuations of a BTZ Black Hole in Massive Gravity
• Position dependent energy level shifts of an accelerated atom in the presence of a boundary
• Holographic Complexity of Quantum Black Holes
• The Lamb shift in de Sitter spacetime
• Lamb Shift for static atoms outside a Schwarzschild black hole
• Modification of energy shifts of atoms by the presence of a boundary in a thermal bath and the Casimir-Polder force
• Comments on the anti-Hawking effect on a BTZ black hole spacetime
• Anti-Hawking Phenomena around a Rotating BTZ Black Hole

Cited by in corpus (3)

• Anisotropic Generalized Polytropic Spheres: Regular 3D Black Holes
• Dissipative dynamics of an open quantum battery in the BTZ spacetime
• Quantum thermal machines in BTZ black hole spacetime