The Lamb shift in the BTZ spacetime

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