On classical super-radiance in Kerr-Newman-anti-de Sitter black holes

TL;DR

This paper investigates classical scalar field modes around Kerr-Newman-anti-de Sitter black holes, analyzing boundary conditions and frequency definitions to determine when super-radiance occurs, revealing its dependence on boundary conditions and frequency choices.

Contribution

It provides a detailed analysis of super-radiance in KN-AdS black holes under different boundary conditions and frequency definitions, clarifying when super-radiance can occur.

Findings

Reflective boundary conditions prevent super-radiance.

Transparent boundary conditions can allow super-radiance depending on frequency choice.

Globally time-like Killing vector leads to no super-radiance with natural positive frequency.

Abstract

We study in detail the modes of a classical scalar field on a Kerr-Newman-anti-de Sitter (KN-AdS) black hole. We construct sets of basis modes appropriate to the two possible boundary conditions (``reflective'' and ``transparent'') at time-like infinity, and consider whether super-radiance is possible. If we employ ``reflective'' boundary conditions, all modes are non-super-radiant. On the other hand, for ``transparent'' boundary conditions, the presence of super-radiance depends on our definition of positive frequency. For those KN-AdS black holes having a globally time-like Killing vector, the natural choice of positive frequency leads to no super-radiance. For other KN-AdS black holes, there is a choice of positive frequency which gives no super-radiance, but for other choices there will, in general, be super-radiance.