Time-domain metric reconstruction for self-force applications

Abstract

We present a new method for calculation of the gravitational self-force (GSF) in Kerr geometry, based on a time-domain reconstruction of the metric perturbation from curvature scalars.

In our new approach, which relies on foundation work laid out by Pound et al. in [Phys. Rev. D 89, 024009 (2014)], the GSF is computed directly from a scalar-like selfpotential that satisfies the time-domain Teukolsky equation on the Kerr background. The metric perturbation from which the GSF is derived has a gauge discontinuity on a closed sphere r = rp(t), where rp(t) is the Boyer-Lindquist (possibly time-dependent) radial location of the particle. The crucial step in our method involves the formulation of suitable junction conditions for the metric perturbation at rp(t), which we do here for generic orbits in Kerr.

The new approach is computationally less intensive than existing time-domain methods, which rely on a direct integration of the linearised Einstein’s equations and are impaired by mode instabilities. At the same time, it retains the utility and flexibility of a time-domain treatment, allowing calculations for any type of orbit (including highly eccentric or unbound ones) and the possibility of self-consistently evolving the orbit under the effect of the GSF.

For a first applications of our method, we consider circular geodesic orbits in Schwarzschild geometry, and then circular equatorial geodesic orbits in Kerr. For these cases we present a full numerical implementation, comparing results with those obtained using established frequency-domain methods, and also with analytical solutions where available. We finally lay out a roadmap for further applications of the method.

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Identifiers

ORCID for Leor Barack: orcid.org/0000-0003-4742-9413

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