Quantization of AdS_3 Black Holes in External Fields

TL;DR

The paper develops a holographic, boundary-based description of AdS3 black hole microphysics in the presence of an external scalar field. By recasting 3D gravity as a CS theory with a boundary WZW (and ultimately Liouville) description, the external field induces a boundary perturbation by a primary operator with weights (1,1), enabling microscopic computation of black hole transition rates. The BTZ black hole is shown to correspond to a thermal state in the boundary CFT, and detailed balance yields Hawking radiation with greybody factors, matching semiclassical results. The approach is explicit for AdS3 and has implications for higher dimensional black holes whose near-horizon geometry contains AdS3, without relying on string theory or AdS/CFT conjecture. The results provide a gravitationally grounded mechanism for black hole radiance based on boundary dynamics.

Abstract

2+1-dimensional Anti-deSitter gravity is quantized in the presence of an external scalar field. We find that the coupling between the scalar field and gravity is equivalently described by a perturbed conformal field theory at the boundary of AdS_3. We derive the explicit form of this coupling, which allows us to perform a microscopic computation of the transition rates between black hole states due to absorption and induced emission of the scalar field. Detailed thermodynamic balance then yields Hawking radiation as spontaneous emission, and we find agreement with the semiclassical result, including greybody factors. This result also has application to four and five dimensional black holes in supergravity. However, since we only deal with gravitational degrees of freedom, the approach is not based on string theory, and does not depend, either, on the validity of Maldacena's AdS/CFT conjecture.