A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

TL;DR

This paper rigorously analyzes energy extraction from a rotating black hole using scalar waves, mathematically confirming superradiance and quantifying energy gain within Kerr geometry.

Contribution

It provides a rigorous mathematical framework for superradiance in Kerr black holes and quantifies energy extraction using wave packets.

Findings

Energy can be extracted from Kerr black holes via superradiance.

The maximal energy gain from the black hole is quantified.

The change in mass and angular momentum aligns with classical results.

Abstract

The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou's result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator.