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A Transport Equation Approach to Green Functions and Self-force Calculations

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Wardell,  Barry
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1003.0476
(Preprint), 214KB

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Citation

Wardell, B., & Ottewill, A. C. (2012). A Transport Equation Approach to Green Functions and Self-force Calculations. In T. Damour, R. T. Jantzen, & R. Ruffini (Eds.), The Twelfth Marcel Grossmann Meeting: On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories (pp. 838-840). World Scientific.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-9D4B-2
Abstract
In a recent work, we presented the first application of the Poisson-Wiseman-Anderson method of `matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function which are respectively valid in the `quasilocal' and `distant past' regimes, and which may be matched together within the normal neighbourhood. In this article, we introduce the method of matched expansions and discuss transport equation methods for the calculation of the Green function in the quasilocal region. These methods allow the Green function to be evaluated throughout the normal neighborhood and are also relevant to a broad range of problems from radiation reaction to quantum field theory in curved spacetime and quantum gravity.