Conformal Invariance and Near-extreme Rotating AdS Black Holes

TL;DR

This paper derives Green's functions for scalar fields in near-extreme rotating AdS black holes, revealing conformal invariance through the reduction of the radial equation to a Hypergeometric form with SL(2,R)^2 symmetry.

Contribution

It demonstrates how the radial equation simplifies to a Hypergeometric form in a specific scaling limit, uncovering conformal invariance in near-extreme rotating black holes.

Findings

Radial equation reduces to Hypergeometric form in the scaling limit.

SL(2,R)^2 symmetry indicates underlying conformal invariance.

Explicit Green's functions for scalar fields in this background.

Abstract

We obtain retarded Green's functions for massless scalar fields in the background of near-extreme, near-horizon rotating charged black holes of five-dimensional minimal gauged supergravity. The radial part of the (separable) massless Klein-Gordon equation in such general black hole backgrounds is Heun's equation, due to the singularity structure associated with the three black hole horizons. On the other hand, we find the scaling limit for the near-extreme, near-horizon background where the radial equation reduces to a Hypergeometric equation whose $SL(2,{\bf R})^2$ symmetry signifies the underlying two-dimensional conformal invariance, with the two sectors governed by the respective Frolov-Thorne temperatures.