Correlation Functions and Hidden Conformal Symmetry of Kerr Black Holes

TL;DR

This paper extends the understanding of scalar three-point correlators in Kerr black holes beyond extremal cases, providing evidence for a dual conformal field theory description and proposing a general method for finite-temperature correlators.

Contribution

It generalizes the calculation of extremal three-point functions to non-extremal Kerr black holes and introduces a new recipe for finite-temperature correlator computations.

Findings

Correlators match dual CFT predictions in extended Kerr cases

Proposed a universal method for finite-temperature correlator calculations

Identified conditions under which extremal couplings vanish

Abstract

Extremal scalar three-point correlators in the near-NHEK geometry of Kerr black holes have recently been shown to agree with the result expected from a holographically dual non-chiral two-dimensional conformal field theory. In this paper we extend this calculation to extremal three-point functions of scalars in a general Kerr black hole which need not obey the extremality condition $M=\sqrt{J}$. It was recently argued that for low frequency scalars in the Kerr geometry there is a dual conformal field theory description which determines the interactions in this regime. Our results support this conjecture. Furthermore, we formulate a recipe for calculating finite-temperature retarded three-point correlation functions which is applicable to a large class of (even non-extremal) correlators, and discuss the vanishing of the extremal couplings.