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

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.