Covariant and coordinate punctures for 2nd-order gravitational self-force in a highly regular gauge @LISAcommunity

Uploaded July 2022 | Updated September 2026, 1 hour ago

Second-order gravitational self-force (2GSF) is the primary way of modelling extreme-mass-ratio inspirals (EMRIs). These are an important class of gravitational wave sources for the future space-based detector the Laser Interferometer Space Antenna (LISA). In an EMRI, a compact object of ~10 solar masses spirals into a supermassive black hole, ~10^6 solar masses, over the course of a year. One difficulty that appears in self-force calculations is dealing with the strong divergence that occurs near the worldline of the small object, causing both numerical and analytical issues. Previous work demonstrated that this could be alleviated within a class of highly regular gauges and also presented the metric perturbation in these gauges in a local coordinate form. We build on this previous work using methods developed for Lorenz gauge 2GSF calculations to derive expressions for the highly regular gauge metric perturbations in both fully covariant form and in a generic coordinate expansion. These results could then be used as input into a puncture scheme or two-timescale expansion in order to solve the field equations.

Authors: Samuel Upton, Adam Pound
Presenter: Samuel Upton

Covariant and coordinate punctures for 2nd-order gravitational self-force in a highly regular gauge

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