A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

Details A Rigorous Treatment of Energy Extraction from a Rotating Black Hole A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

2007-01-01

arxiv.org/abs/gr-qc/0701018v3

Commun.Math.Phys. 287 (2009) 829-847

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, LaTeX, proof of Propositions 2.3 and 3.1 given in more detail

Scientific paper

10.1007/s00220-009-0730-7

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.

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