Instabilities of Kerr-AdS_5 x S^5 Spacetime

TL;DR

This paper investigates the classical instabilities of Kerr-AdS_5 x S^5 spacetime, identifying superradiant and Gregory-Laflamme instabilities, and discusses their implications for the phase structure and AdS/CFT correspondence.

Contribution

It provides a detailed analysis of the instabilities in Kerr-AdS_5 x S^5 spacetime, revealing new insights into its phase structure and symmetry breaking mechanisms.

Findings

Identified superradiant and Gregory-Laflamme instabilities.

Analyzed the impact of instabilities on phase structure.

Discussed implications for AdS/CFT correspondence.

Abstract

We study gravitational perturbations of the Kerr-AdS_5 x S^5 spacetime with equal angular momenta. In this spacetime, we found the two kinds of classical instabilities, superradiant and Gregory-Laflamme instabilities. The superradiant instability is caused by the wave amplification via superradiance, and by wave reflection due to the potential barrier of the AdS spacetime. The Gregory-Laflamme instability appears in Kaluza-Klein modes of the internal space S^5 and breaks the symmetry SO(6). Taken into account these instabilities, the phase structure of Kerr-AdS_5 x S^5 spacetime is revealed. The implication for the AdS/CFT correspondence is also discussed.