Abstract:
The challenge of computing `selfconsistent' orbital evolutions, in which the historic motion departs from a geodesic of the background spacetime, has motivated much work on accurate timedomain schemes for selfforce 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 secondorder PDEs), in which the particle is handled with a puncture based on the DetweilerWhiting 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 centreofmass induced by the particle) and substantial gauge freedom. Unfortuantely, the Lorenzgauge formulation appears to be susceptible to puregauge 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 gaugedriver which works works for special case of circular orbits, and discuss possible generalizations for the future.
