Gravitational dynamics of near-extreme Kerr (Anti-)de Sitter black holes

TL;DR

This paper investigates the thermodynamic behavior and near-horizon dynamics of near-extremal Kerr (Anti-)de Sitter black holes, revealing that their perturbations are governed by a Schwarzian theory and highlighting differences among extremal scenarios.

Contribution

It provides a detailed analysis of near-extremal Kerr (Anti-)de Sitter black holes, identifying the governing Schwarzian dynamics and contrasting different extremal cases with new geometric insights.

Findings

Perturbations near extremality are governed by a Schwarzian theory.

Different extremal scenarios exhibit distinct near horizon geometries.

Thermodynamics in 4D reflects in near horizon dynamics, especially in the Ultracold case.

Abstract

We analyze the thermodynamic response near extremality of black holes with angular momentum in (3+1)-dimensional de Sitter and Anti-de Sitter spacetimes. While Kerr-AdS$_4$ is characterized by a single extremal limit, for Kerr-dS$_4$ there are three different extremal scenarios (Cold, Nariai and Ultracold). These exhibit different near horizon geometries, with AdS$_2$, dS$_2$ and Mink$_2$ factors respectively. We analyze each extremal case and contrast the response once the black holes are taken out of extremality. We study the perturbations of the near horizon geometry at the level of the 4D metric, considering a consistent truncation for the metric fluctuations, and find solutions to the linearized Einstein equations. We characterize the perturbations that are responsible for the deviations away from extremality and show that their dynamics is governed by a Schwarzian theory. We treat the Ultracold case separately, detailing how the thermodynamics in 4D is reflected in the near horizon dynamics.