Superradiance Instability of Small Rotating AdS Black Holes in Arbitrary Dimensions

TL;DR

This paper analytically demonstrates that small rotating AdS black holes in any dimension are unstable to superradiance, extending previous results and confirming the instability across a broad class of black hole solutions.

Contribution

It provides an analytical proof of superradiance instability for small rotating AdS black holes in arbitrary dimensions, regardless of angular momentum quantum number.

Findings

Superradiance instability occurs in small rotating AdS black holes in all dimensions.

Analytical solutions confirm the instability for any angular momentum quantum number.

Results agree with the black hole bomb formalism in the appendix.

Abstract

We investigate the stability of $D$ dimensional singly rotating Myers-Perry-AdS black holes under superradiance against scalar field perturbations. It is well known that small four dimensional rotating or charged Anti-de Sitter (AdS) black holes are unstable against superradiance instability of a scalar field. Recent works extended the existence of this instability to five dimensional rotating charged AdS black holes or static charged AdS black holes in arbitrary dimensions. In this work we analytically prove that, rotating small AdS black holes in arbitrary dimensions also show superradiance instability irrespective of the value of the (positive) angular momentum quantum number. To do this we solve the Klein-Gordon equation in the slow rotation, low frequency limit. By using the asymptotic matching technique, we are able to calculate the real and imaginary parts of the correction terms to the frequency of the scalar field due to the presence of the black hole, confirming the presence of superradiance instability. We see that, unlike in the case of static AdS black holes, the analytical method is valid for rotating AdS black holes for any value of angular momentum number and space-time dimensions. For comparison we derive the corresponding correction terms for Myers-Perry black holes in the black hole bomb formalism in Appendix and see that the results are in agreement.