15th Capra Meeting on Radiation Reaction in General Relativity

High-order expansions of the Detweiler-Whiting Singular Field

Anna Heffernan

University College Dublin
[SLIDES]

The self field of a charged particle has a component that diverges at the particle. We use both coordinate and covariant approaches to compute an expansion of this singular field for generic geodesic orbits in Schwarzschild space-time for scalar, electromagnetic and gravitational cases. We check agreement of both approaches and give, as an application, the calculation of previously unknown regularization parameters. In this so-called "mode-sum regularization" approach, each mode of the field is finite, while their sum diverges. The sum may be rendered finite and convergent by the subtraction of "regularisation parameters". higher order parameters lead to faster convergence int eh mode-sum. As a second example application, we compute high order expressions for the effective sourve approach to self-force calculations.