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- W1558430198 abstract "If a small of mass $mu M$ (with $mu ll 1$) orbits a Schwarzschild or Kerr black hole of mass $M$, the particle is subject to an $O(mu)$ radiation-reaction Here I argue that it's valuable to compute this self-force highly accurately (relative error of $ltsim 10^{-6}$) and efficiently, and I describe techniques for doing this and for obtaining and validating error estimates for the computation. I use an adaptive-mesh-refinement (AMR) time-domain numerical integration of the perturbation equations in the Barack-Ori mode-sum regularization formalism; this is efficient, yet allows easy generalization to arbitrary particle orbits. I focus on the model problem of a scalar particle in a circular geodesic orbit in Schwarzschild spacetime. The mode-sum formalism gives the self-force as an infinite sum of regularized spherical-harmonic modes $sum_{ell=0}^infty F_{ell,reg}$, with $F_{ell,reg}$ (and an error estimate) computed numerically for $ell ltsim 30$ and estimated for larger~$ell$ by fitting an asymptotic series. Here I validate the internal error estimates for the individual $F_{ell,reg}$ using a large set of numerical self-force computations of widely-varying accuracies. I present numerical evidence that the actual numerical errors in $F_{ell,reg}$ for different~$ell$ are at most weakly correlated, so the usual statistical error estimates are valid for computing the self-force. I show that the tail fit is numerically ill-conditioned, but this can be mostly alleviated by renormalizing the basis functions to have similar magnitudes. Using AMR, fixed mesh refinement, and extended-precision floating-point arithmetic, I obtain the (contravariant) radial component of the self-force for a particle in a circular geodesic orbit of areal radius $r = 10M$ to within $1$~ppm relative error." @default.
- W1558430198 created "2016-06-24" @default.
- W1558430198 creator A5064902135 @default.
- W1558430198 date "2010-06-18" @default.
- W1558430198 modified "2023-09-27" @default.
- W1558430198 title "Highly accurate and efficient self-force computations using time-domain methods: Error estimates, validation, and optimization" @default.
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