Superradiance in the BTZ black hole with Robin boundary conditions

TL;DR

This paper demonstrates the existence of superradiant modes for massive scalar fields in BTZ black holes under Robin boundary conditions, revealing new energy dynamics distinct from traditional superradiance scenarios.

Contribution

It introduces Robin boundary conditions at infinity as a novel setting for superradiance in BTZ black holes, showing that not all growing modes are due to energy extraction.

Findings

Superradiant modes exist under Robin boundary conditions.

Some modes grow due to bulk instability, not superradiance.

Low-frequency bosonic modes can pump energy into the black hole.

Abstract

We show the existence of superradiant modes of massive scalar fields propagating in BTZ black holes when certain Robin boundary conditions, which never include the commonly considered Dirichlet boundary conditions, are imposed at spatial infinity. These superradiant modes are defined as those solutions whose energy flux across the horizon is towards the exterior region. Differently from rotating, asymptotically flat black holes, we obtain that not all modes which grow up exponentially in time are superradiant; for some of these, the growth is sourced by a bulk instability of AdS3, triggered by the scalar field with Robin boundary conditions, rather than by energy extraction from the BTZ black hole. Thus, this setup provides an example wherein Bosonic modes with low frequency are pumping energy into, rather than extracting energy from, a rotating black hole.