On Calculating Self-force for Radiating Systems
Andrew Norton
(Max Planck Institute for Gravitational Physics, Germany)
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The self-force on a radiating system can be calculated by considering energy-momentum balance across a worldtube that encloses the system. For example, such tube-based calculations have been done in a curved background spacetime for the electromagnetic self-force on a point-like charge (DeWitt and Brehme 1960, Hobbs 1968) and for the gravitational self-force on a point-like mass (Mino, Sasaki and Tanaka 1997). Until recently, however, all tube-based self-force calculations have followed the steps taken in Dirac's 1938 calculation of the electromagnetic self-force for the classical radiating electron. In particular, they have invoked a "classical mass renormalization" as the radius of the worldtube goes to zero. This step is mathematically ill defined and physically nonsensical. It involves the subtraction of divergent quantities and ascribes an infinite negative "bare mass" to to the system. Nevertheless, it gives the right answer! I shall explain why, by showing how tube-based self-force calculations can be done properly, that is, for systems of finite size and without invoking a mass renormalization. The talk is based on published results (Class. Quantum Grav. 26 (2009) 105009), but if time permits I shall also describe some recent applications and examples.