Implementation of a GHZ-Teukolsky puncture scheme for gravitational self-force calculations

Abstract

Post-adiabatic models of extreme- and intermediate-mass-ratio inspirals will require calculations of second-order gravitational self-force effects in the spacetime of a spinning, Kerr black hole. We take a step toward such calculations by implementing the recently formulated Teukolsky puncture scheme with Green-Hollands-Zimmerman metric reconstruction [CQG 39, 015019 (2022)]. This scheme eliminates the critical obstacle of gauge singularities that arise in the standard no-string metric reconstruction. Our first proof-of-principle implementation is limited to the simple case of circular orbits in Schwarzschild spacetime, but the method also applies to generic orbits on a Kerr background. We conclude with a discussion of various approaches to the second-order self-force problem in Kerr.

31 pages, 9 figures

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• Sourced metric perturbations of Kerr spacetime in Lorenz gauge
• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• Simple, efficient method of calculating the Detweiler-Whiting singular field to very high order
• Metric reconstruction and the Hamiltonian for eccentric, precessing binaries in the small-mass-ratio limit
• Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime