Holographic description of Kerr-Bolt-AdS-dS Spacetimes

TL;DR

This paper demonstrates a holographic duality between Kerr-Bolt-AdS-dS black holes and 2D conformal field theories, establishing a correspondence through wave equations, scattering amplitudes, and entropy calculations.

Contribution

It provides the first detailed holographic description of Kerr-Bolt-AdS-dS spacetimes, including extremal and non-extremal cases, via wave equations and conformal symmetry analysis.

Findings

Wave equations in near-horizon regions match $SL(2,R)$ Casimir.

Scattering amplitudes agree with CFT predictions.

Microscopic entropy matches Bekenstein-Hawking entropy.

Abstract

We show that there exists a holographic 2D CFT description of a Kerr-Bolt-AdS-dS spacetime. We first consider the wave equation of a massless scalar field propagating in extremal Kerr-Bolt-AdS-dS spacetimes and find in the "near region", the wave equation in extremal limit could be written in terms of the $SL(2,R)$ quadratic Casimir. This suggests that there exist dual CFT descriptions of these black holes. In the probe limit, we compute the scattering amplitudes of the scalar off the extremal black holes and find perfect agreement with the CFT prediction. Furthermore we study the holographic description of the generic four dimensional non-extremal Kerr-Bolt-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could still be rewritten as the $SL(2,R)$ quadratic Casimir, suggesting the existence of dual 2D description. We read the temperatures of the dual CFT from the conformal coordinates and obtain the central charges by studying the near-horizon geometry of near-extremal black holes. We recover the macroscopic entropy from the microscopic counting. We also show that for the superradiant scattering, the retarded Green's functions and the corresponding absorption cross sections are in perfect match with CFT prediction.