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Global spectral representations of black hole spacetimes in the complex plane

Maurice H. P. M. van Putten
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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 $M/s$, 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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Maurice H. P. M. van Putten. 2005-06-09. Global spectral representations of black hole spacetimes in the complex plane. https://doi.org/10.1073/pnas.0508406103

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