High-order expansions of the Detweiler-Whiting singular field in Schwarzschild spacetime

Details High-order expansions of the Detweiler-Whiting singular field in Schwarzschild spacetime High-order expansions of the Detweiler-Whiting singular field in Schwarzschild spacetime

2012-04-03

arxiv.org/abs/1204.0794v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

38 pages

Scientific paper

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 spacetime for scalar, electromagnetic and graviational cases. We check agreement of both approaches and give, as an application, the calculation of previously unknown regularisation 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 "regularization parameters". Higher order parameters lead to faster convergence in the mode-sum. As a second example application, we compute high order expressions for the effective source approach to self-force calculations.

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