Two-timescale adiabatic expansion of a scalar field model

Abstract

The analysis of gravitational wave data may require greater accuracy than is afforded by the adiabatic approximation to the trajectory of and field produced by a particle moving in curved spacetime. Higher accuracy is available with a two-timescale approach using as an expansion parameter the ratio of orbital time to radiation reaction time. To avoid apparent divergences at large distances, the details of the method are important, especially the choice of the foliation, the spacetime surfaces on which the orbital elements are taken to be constant. Here we apply the two-timescale approach to a simple linear model to demonstrate the details of the method. In particular we use it to show that a null foliation avoids large-distance divergences in the first-order post-adiabatic approximation, and we argue that this will be true more generally for a null foliation.

References in corpus (7)

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Cited by in corpus (12)

• The motion of point particles in curved spacetime
• Self-force and radiation reaction in general relativity
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Transient resonances in the inspirals of point particles into black holes
• The self-consistent gravitational self-force
• Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime
• Black hole perturbation theory and gravitational self-force
• Fast Self-forced Inspirals
• Second-order perturbation theory: problems on large scales
• Hamiltonians and canonical coordinates for spinning particles in curved space-time
• Singular perturbation techniques in the gravitational self-force problem
• Motion of small bodies in general relativity: foundations and implementations of the self-force