On the gravitational stability of D1-D5-P black holes

TL;DR

This work studies the stability of nonextremal D1-D5-P black holes with respect to superradiant instabilities by analyzing minimally coupled scalar perturbations in a six-dimensional background that includes the noncompact space and the $S^1$ circle. By separating the Klein-Gordon equation into angular and radial parts and recasting the radial equation as a Schrödinger problem with potentials $V_\pm(r)$, the authors search for bound states that could trigger superradiant instabilities; they find no such bound states for both massless and small-mass scalars, even when KK momentum ($\lambda \neq 0$) is present. The results imply that these black holes are not superradiantly unstable, in contrast to the ergoregion instability found for the horizon-free JMaRT solitons, and they discuss the implications for Mathur’s fuzzball proposal, including the interpretation that typical non-BPS microstates may differ from the highly symmetric JMaRT solutions and could possess long-timescale instabilities or require a broader microstate ensemble. Overall, the paper provides evidence that nonextremal D1-D5-P black holes are dynamically stable against the specific superradiant mechanism considered, contributing to our understanding of microstate geometries and their role in the fuzzball picture.

Abstract

We examine the stability of the nonextremal D1-D5-P black hole solutions. In particular, we look for the appearance of a superradiant instability for the spinning black holes but we find no evidence of such an instability. We compare this situation with that for the smooth soliton geometries, which were recently observed to suffer from an ergoregion instability, and consider the implications for the fuzzball proposal.

Figures (3)

• Figure 1: Typical Schrödinger potentials for the black hole branch, $M\geq (a_1+a_2)^2$ or $r_+^2>0$, and for modes with no KK momentum, $\lambda=0$. Figure a) refers to the case $m_{\psi}>0$, while figure b) corresponds to case $m_{\psi}<0$. Superradiant modes (dashed line) with $|\omega|< |\omega_{\rm sup}|$ do exist but there are no trapped bound states and thus the geometry is not afflicted by the superradiant instability.
• Figure 2: Examples of potentials that would correspond to black hole geometries afflicted by the superradiant instability. Unstable modes are superradiant modes with $|\omega|< |\omega_{\rm sup}|$ that are also bound states (dashed line). Case $a$) corresponds to $\lambda=0$ while case $b$) corresponds to $\lambda\neq 0$.
• Figure 3: Black hole branch, $M\geq (a_1+a_2)^2$ or $r_+^2>0$, for modes with KK momentum, $\lambda\neq 0$. Although the KK momentum provides a barrier at infinity, it is not able to create bound states where superradiant unstable modes could eventually live.