Static self-forces in arbitrary dimensions

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Written by Abraham Harte

This talk discusses forces and torques acting on static extended bodies in static spacetimes with any number of dimensions. Non-perturbatively, these results have the same form in all dimensions. Meaningful point particle limits are quite different, however. Such limits are defined and evaluated, resulting in simple "regularization algorithms" which can be used in concrete calculations. In them, self-interaction is shown to be progressively less important in higher numbers of dimensions; it generically competes in magnitude with increasingly high-order extended-body effects. Conversely, we show that self-interaction effects can be relatively large in 1+1 and 2+1 dimensions. The static self-force problem in arbitrary dimensions provides a useful testbed with which to continue the development of general, non-perturbative methods in the theory of motion. Several new insights are obtained in this direction, including a significantly improved understanding of the renormalization process. Much of this also generalizes to the dynamical regime.