Global spectral representations of black hole spacetimes in the complex plane

Details Global spectral representations of black hole spacetimes in the complex plane Global spectral representations of black hole spacetimes in the complex plane

2005-06-09

arxiv.org/abs/gr-qc/0506052v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Based on an invited talk at the Int'l Conf. Theor. Physics, 11-16 April 2005, Lebedev Physical Institute, Moscow

Scientific paper

10.1073/pnas.0508406103

Binary black hole coalescence produces a finite burst of gravitational radiation which propagates towards quiescent infinity. These spacetimes are analytic about infinity and contain a dimensionless coupling constant $M/s$, where $M$ denotes the total mass-energy and $s$ an imaginary distance. This introduces globally convergent Fourier series on a complex radial coordinate, allowing spectral representation of black hole spacetimes in all three dimensions. We illustrate this representation theory on a Fourier-Legendre expansion of Boyer-Lindquist initial data and a scalar wave equation with signal recovery by Cauchy's integral formula.

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