A Rigorous Treatment of Energy Extraction from a Rotating Black Hole
arXiv:gr-qc/0701018 · doi:10.1007/s00220-009-0730-7
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.
19 pages, LaTeX, proof of Propositions 2.3 and 3.1 given in more detail
References in corpus (1)
Cited by in corpus (8)
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- Superradiance in Modified Gravity (MOG)
- Superradiance in the BTZ black hole with Robin boundary conditions
- On the Use of Multipole Expansion in Time Evolution of Non-linear Dynamical Systems and Some Surprises Related to Superradiance
- Superradiance initiated inside the ergoregion
- A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes
- Lectures on Linear Stability of Rotating Black Holes
- Energy Extraction, or Lack Thereof