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A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

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arxiv gr-qc/0701018 v3 pith:NN3DLDHV submitted 2007-01-01 gr-qc math-phmath.MP

Felix Finster , Niky Kamran , Joel Smoller , Shing-Tung Yau This is my paper · ORCID
classification gr-qcmath-phmath.MP
keywords waveblackenergyholemathematicalpenroseprocessrigorous
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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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  1. On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes

    gr-qc 2025-07 conditional novelty 4.0 of 10

    For subextremal Kerr spacetimes, the paper constructs a positive-definite, conserved Hamiltonian energy for axially symmetric linear perturbations, indicating a form of linear stability within this symmetry class.

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