Hawking radiation for a scalar field conformally coupled to an AdS black hole

TL;DR

This paper analyzes Hawking radiation for a conformally coupled scalar field in an AdS black hole background, using mode decomposition and the Damour-Ruffini method to relate radial behavior to particle emission.

Contribution

It derives a simplified Heun equation for the scalar field modes due to conformal invariance and connects the radial critical exponent to Hawking radiation.

Findings

Heun equation with simple coefficients obtained

Radial critical exponent related to Hawking radiation

Method applicable to conformally coupled scalar fields in AdS black holes

Abstract

The decomposition in normal modes of a scalar field conformally coupled to an AdS black hole leads to a Heun equation with simple coefficients thanks to conformal invariance. By applying the Damour-Ruffini method we can relate the critical exponent of the radial part at the horizon surface to the Hawking radiation of scalar particles.