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

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.

Figure 1

Typical Schrödinger potentials for the black hole branch, $M\ge (a_1+a_2{)}^2$ or $r_{+}^2>0$, and for modes with no KK momentum, $\lambda =0$. Figure (a) refers to the case $m_{\psi }>0$, while Fig. (b) corresponds to the case $m_{\psi }<0$. Superradiant modes (dashed line) with $|\omega |<|{\omega }_{\sup }|$ 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 $|\omega |<|{\omega }_{\sup }|$ that are also bound states (dashed line). Case (a) corresponds to $\lambda =0$ while case (b) corresponds to $\lambda \ne 0$.

Figure 3

Black hole branch, $M\ge (a_1+a_2{)}^2$ or $r_{+}^2>0$, for modes with KK momentum, $\lambda \ne 0$. Although the KK momentum provides a barrier at infinity, it is not able to create bound states where superradiant unstable modes could eventually live.