Analytic structure of radiation boundary kernels for blackhole perturbations

Abstract

Exact outer boundary conditions for gravitational perturbations of the Schwarzschild metric feature integral convolution between a time-domain boundary kernel and each radiative mode of the perturbation. For both axial (Regge–Wheeler) and polar (Zerilli) perturbations, we study the Laplace transform of such kernels as an analytic function of (dimensionless) Laplace frequency. We present numerical evidence indicating that each such frequency-domain boundary kernel admits a “sum-of-poles” representation. Our work has been inspired by Alpert, Greengard, and Hagstrom’s analysis of nonreflecting boundary conditions for the ordinary scalar wave equation.