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. 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.