Accelerated motion and the self-force in Schwarzschild spacetime

Abstract

We provide expansions of the Detweiler-Whiting singular field for motion along arbitrary, planar accelerated trajectories in Schwarzschild spacetime. We transcribe these results into mode-sum regularization parameters, computing previously unknown terms that increase the convergence rate of the mode-sum. We test our results by computing the self-force along a variety of accelerated trajectories. For non-uniformly accelerated circular orbits we present results from a new 1+1D discontinuous Galerkin time-domain code which employs an effective-source. We also present results for uniformly accelerated circular orbits and accelerated bound eccentric orbits computed within a frequency-domain treatment. Our regularization results will be useful for computing self-consistent self-force inspirals where the particle's worldline is accelerated with respect to the background spacetime.

19 pages, 6 figures (accepted CQG special issue article version)

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• Slow evolution of the metric perturbation due to a quasicircular inspiral into a Schwarzschild black hole
• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
• Gravitational self-force corrections to tidal invariants for spinning particles on circular orbits in a Schwarzschild spacetime
• Worldtube excision method for intermediate-mass-ratio inspirals: self-consistent evolution in a scalar-charge model
• Regularization of a scalar charged particle for generic orbits in Kerr spacetime
• Eternal binaries
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• Adiabatic evolution due to the conservative scalar self-force during orbital resonances