Unbound motion on a Schwarzschild background: Practical approaches to frequency domain computations

Abstract

Gravitational perturbations due to a point particle moving on a static black hole background are naturally described in Regge-Wheeler gauge. The first-order field equations reduce to a single master wave equation for each radiative mode. The master function satisfying this wave equation is a linear combination of the metric perturbation amplitudes with a source term arising from the stress-energy tensor of the point particle. The original master functions were found by Regge and Wheeler (odd parity) and Zerilli (even parity). Subsequent work by Moncrief and then Cunningham, Price and Moncrief introduced new master variables which allow time domain reconstruction of the metric perturbation amplitudes. Here I explore the relationship between these different functions and develop a general procedure for deriving new higher-order master functions from ones already known. The benefit of higher-order functions is that their source terms always converge faster at large distance than their lower-order counterparts. This makes for a dramatic improvement in both the speed and accuracy of frequency domain codes when analyzing unbound motion.

12 pages, 3 figures

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• Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
• Time-domain metric reconstruction for hyperbolic scattering
• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
• Frequency-domain approach to self-force in hyperbolic scattering
• Accelerated motion and the self-force in Schwarzschild spacetime
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• Gravitational radiation from a particle plunging into a Schwarzschild black hole: frequency-domain and semirelativistic analyses
• Hyperboloidal method for frequency-domain self-force calculations