Superradiance on the Reissner-Nordstrom metric

TL;DR

This paper investigates superradiance phenomena for charged scalar fields around Reissner-Nordstrom black holes, demonstrating energy extraction mechanisms, numerical behaviors similar to Penrose process, and stability indications of the black hole.

Contribution

It introduces a geometric measure of energy extraction, provides numerical simulations of superradiant behavior, and explores stability of the Reissner-Nordstrom metric.

Findings

Energy can be extracted via superradiance, exceeding initial wave energy.

Numerical simulations show behavior analogous to the Penrose process.

No hyperradiant behavior observed, indicating linear stability.

Abstract

In this article, we study the superradiance of charged scalar fields on the sub-extremal Reissner-Nordstrom metric, a mechanism by which such fields can extract energy from a static spherically symmetric charged black hole. A geometrical way of measuring the amount of energy extracted is proposed. Then we investigate the question numerically. The toy-model and the numerical methods used in our simulations are presented and the problem of long time measurement of the outgoing energy flux is discussed. We provide a numerical example of a field exhibiting a behaviour analogous to the Penrose process: an incoming wave packet which splits, as it approaches the black hole, into an incoming part with negative energy and an outgoing part with more energy than the initial incoming one. We also show another type of superradiant solution for which the energy extraction is more important. Hyperradiant behaviour is not observed, which is an indication that the Reissner-Nordstrom metric is linearly stable in the sub-extremal case.