Analytic structure of radiation boundary kernels for blackhole perturbations

TL;DR

This paper investigates the analytic structure of radiation boundary kernels for black hole perturbations, revealing they can be represented as sums of poles, which aids in understanding boundary conditions in gravitational wave simulations.

Contribution

It provides a detailed analysis of the Laplace transform of boundary kernels for Schwarzschild perturbations, showing they admit a sum-of-poles representation, inspired by scalar wave boundary condition studies.

Findings

Boundary kernels can be expressed as sums of poles.

Numerical evidence supports the sum-of-poles representation.

The work enhances understanding of boundary conditions in black hole 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.