Quantization of AdS_3 Black Holes in External Fields

TL;DR

This paper quantizes 2+1-dimensional AdS_3 black holes with an external scalar field, deriving a boundary CFT coupling, and computes Hawking radiation microscopically, matching semiclassical results without relying on string theory or AdS/CFT.

Contribution

It introduces a novel quantization approach for AdS_3 black holes with external fields, explicitly deriving boundary couplings and computing transition rates microscopically.

Findings

Derived the boundary coupling between scalar field and gravity.

Computed black hole transition rates due to scalar absorption and emission.

Confirmed Hawking radiation matches semiclassical predictions, including greybody factors.

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.