Accelerated motion and the self-force in Schwarzschild spacetime

TL;DR

This paper advances the calculation of the self-force on particles in Schwarzschild spacetime by deriving new regularization parameters for accelerated trajectories, improving convergence and enabling more accurate modeling of inspirals.

Contribution

It provides new mode-sum regularization parameters for accelerated motions, including previously unknown terms, and demonstrates their application through numerical computations.

Findings

Derived new regularization parameters for accelerated trajectories

Improved convergence rates in self-force calculations

Validated results with numerical simulations for various orbits

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.