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.

revtex4, 14 pages, 12 figures, 3 tables

References in corpus (2)

• Black hole entropy from Quantum Geometry
• Path Integral Over Black Hole Fluctuations

Cited by in corpus (21)

• Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
• Binary black hole merger in the extreme mass ratio limit
• Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis
• A Finite Element Computation of the Gravitational Radiation emitted by a Point-like object orbiting a Non-rotating Black Hole
• Implementation of higher-order absorbing boundary conditions for the Einstein equations
• Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries
• Improved outer boundary conditions for Einstein's field equations
• Asymptotics of Schwarzschild black hole perturbations
• On the accretion-induced QNM excitation of a Schwarzschild black hole
• Boundary conditions for coupled quasilinear wave equations with application to isolated systems
• Dynamical excitation of space-time modes of compact objects
• Persistent junk solutions in time-domain modeling of extreme mass ratio binaries
• Phenomenology and origin of late-time tails in eccentric binary black hole mergers
• Cauchy-perturbative matching revisited: tests in spherical symmetry
• Evolution of scalar fields surrounding black holes on compactified constant mean curvature hypersurfaces
• Boundary Conditions for the Gravitational Field
• Fast evaluation of far-field signals for time-domain wave propagation
• Fast evaluation of asymptotic waveforms from gravitational perturbations
• Toward exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the scalar Teukolsky equation with singular source terms
• The ďAlembert solution in hyperboloidal foliations
• Superconvergent Discontinuous Galerkin Method for the Scalar Teukolsky Equation on Hyperboloidal Domains: Efficient Waveform and Self-Force Computation