15th Capra Meeting on Radiation Reaction in General Relativity

Time-domain schemes for gravitational self-force

Sam Dolan

University of Southampton
[SLIDES]

The challenge of computing `self-consistent' orbital evolutions, in which the historic motion departs from a geodesic of the background spacetime, has motivated much work on accurate time-domain schemes for self-force applications. In this talk I will describe recent progress in the $m$-mode regularization scheme, and progress towards the first calculation of GSF on Kerr. The basis of our scheme is a Z4 formulation of the linearized Einstein equations in Lorenz gauge (i.e. 10 coupled second-order PDEs), in which the particle is handled with a puncture based on the Detweiler-Whiting split. A key challenge for the scheme is handling the low multipoles, which contain both physical content (e.g.~perturbations to mass, angular momentum, and centre-of-mass induced by the particle) and substantial gauge freedom. Unfortuantely, the Lorenz-gauge formulation appears to be susceptible to pure-gauge modes which grow linearly with time. A possible way to stabilize the evolution is to work in a generalized gauge with a (regular) gauge driver. I will demonstrate a gauge-driver which works works for special case of circular orbits, and discuss possible generalizations for the future.