Global spectral representations of black hole spacetimes in the complex plane
arXiv:gr-qc/0506052 · doi:10.1073/pnas.0508406103
Abstract
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 , where denotes the total mass-energy and 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.
Based on an invited talk at the Int'l Conf. Theor. Physics, 11-16 April 2005, Lebedev Physical Institute, Moscow