Global spectral representations of black hole spacetimes in the complex plane
- Massachusetts Institute of Technology–Laser Interferometer Gravitational-Wave Observatory, 175 Albary Street, NW17-161, Cambridge, MA 02139
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Edited by Robert M. Wald, University of Chicago, Chicago, IL, and approved November 17, 2005 (received for review September 26, 2005)
Abstract
Binary black hole coalescence produces a finite burst of gravitational radiation, which propagates toward quiescent infinity. These spacetimes are analytic about infinity and contain a dimensionless coupling constant M/s, where M denotes the total mass-energy and s is an imaginary distance. This work introduces a globally convergent Fourier series in a complex radial coordinate, allowing spectral representations of black hole spacetimes in all three dimensions. This method circumvents singularities associated with black holes and includes infinity, thereby avoiding the need to impose radiative boundary conditions. We illustrate this representation theory on Boyer–Lindquist initial data of two black holes and a scalar wave equation with signal recovery by Cauchy's integral formula.
Footnotes
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↵ † E-mail: mvp{at}ligo.mit.edu.
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Conflict of interest statement: No conflicts declared.
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This paper was submitted directly (Track II) to the PNAS office.
- Copyright © 2006, The National Academy of Sciences
