Regularization of static self-forces

Abstract

Various regularization methods have been used to compute the self-force acting on a static particle in a static, curved spacetime. Many of these are based on Hadamard's two-point function in three dimensions. On the other hand, the regularization method that enjoys the best justification is that of Detweiler and Whiting, which is based on a four-dimensional Green's function. We establish the connection between these methods and find that they are all equivalent, in the sense that they all lead to the same static self-force. For general static spacetimes, we compute local expansions of the Green's functions on which the various regularization methods are based. We find that these agree up to a certain high order, and conjecture that they might be equal to all orders. We show that this equivalence is exact in the case of ultrastatic spacetimes. Finally, our computations are exploited to provide regularization parameters for a static particle in a general static and spherically-symmetric spacetime.

23 pages, no figures

References in corpus (7)

• Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
• Self-force on a scalar particle in a class of wormhole spacetimes
• Self-force of a point charge in the space-time of a symmetric wormhole
• Electrostatic self-interaction in the spacetime of a global monopole with finite core
• Self force of a static electric charge near a Schwarzschild Star
• Electrostatics in a wormhole geometry
• Induced self-energy on a static scalar charged particle in the spacetime of a global monopole with finite core

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• Electrostatics in a simple wormhole revisited
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• Self-force on an arbitrarily coupled static scalar particle in a wormhole space-time
• The inverse spatial Laplacian of spherically symmetric spacetimes
• Self-force and the Schwarzschild star