Small black holes in $AdS_5\times S^5$

TL;DR

This paper investigates the stability of small black holes in the $AdS_5\times S^5$ space, identifying quasinormal modes and demonstrating a Gregory-Laflamme type instability linked to a specific operator.

Contribution

It computes the spectrum of quasinormal modes for black holes in $AdS_5\times S^5$ and explicitly demonstrates the Gregory-Laflamme instability in this setting.

Findings

Recovery of the zero mode previously found by Hubeny and Rangamani

Identification of a Gregory-Laflamme type instability

Connection of instability to a dimension-5 operator expectation value

Abstract

We consider small black holes in $AdS_5\times S^5$, smeared on $S^5$. We compute the spectrum of $\ell \in [1,10]$ $S^5$-quasinormal modes corresponding to fluctuations leading to localization of these black holes on $S^5$. We recover the zero mode found by Hubeny and Rangamani (HR) previously \cite{Hubeny:2002xn}, and explicitly demonstrate that a Gregory-Laflamme type instability is at play in this system. The instability is associated with the expectation value of a dimension-5 operator.