A matched expansion approach to practical self-force calculations

Details A matched expansion approach to practical self-force calculations A matched expansion approach to practical self-force calculations

2005-06-29

arxiv.org/abs/gr-qc/0506136v1

Class.Quant.Grav. 22 (2005) S783-S800

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

IOP style, 8 eps figures, accepted for publication in a special issue of Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/22/15/010

We discuss a practical method to compute the self-force on a particle moving through a curved spacetime. This method involves two expansions to calculate the self-force, one arising from the particle's immediate past and the other from the more distant past. The expansion in the immediate past is a covariant Taylor series and can be carried out for all geometries. The more distant expansion is a mode sum, and may be carried out in those cases where the wave equation for the field mediating the self-force admits a mode expansion of the solution. In particular, this method can be used to calculate the gravitational self-force for a particle of mass mu orbiting a black hole of mass M to order mu^2, provided mu/M << 1. We discuss how to use these two expansions to construct a full self-force, and in particular investigate criteria for matching the two expansions. As with all methods of computing self-forces for particles moving in black hole spacetimes, one encounters considerable technical difficulty in applying this method; nevertheless, it appears that the convergence of each series is good enough that a practical implementation may be plausible.

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