Self-forces from generalized Killing fields

Abstract

A non-perturbative formalism is developed that simplifies the understanding of self-forces and self-torques acting on extended scalar charges in curved spacetimes. Laws of motion are locally derived using momenta generated by a set of generalized Killing fields. Self-interactions that may be interpreted as arising from the details of a body's internal structure are shown to have very simple geometric and physical interpretations. Certain modifications to the usual definition for a center-of-mass are identified that significantly simplify the motions of charges with strong self-fields. A derivation is also provided for a generalized form of the Detweiler-Whiting axiom that pointlike charges should react only to the so-called regular component of their self-field. Standard results are shown to be recovered for sufficiently small charge distributions.

21 pages

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Cited by in corpus (28)

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• High-order expansions of the Detweiler-Whiting singular field in Schwarzschild spacetime
• Second-order perturbation theory: problems on large scales
• Bobbing and Kicks in Electromagnetism and Gravity
• Motion in classical field theories and the foundations of the self-force problem
• Caustics and wave propagation in curved spacetimes
• High-order expansions of the Detweiler-Whiting singular field in Kerr spacetime
• Self force via m-mode regularization and 2+1D evolution: Foundations and a scalar-field implementation on Schwarzschild
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• Effective stress-energy tensors, self-force, and broken symmetry
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• Self-forces on static bodies in arbitrary dimensions
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• Static Self-Forces in a Five-Dimensional Black Hole Spacetime
• Motion of small bodies in general relativity: foundations and implementations of the self-force
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• Hidden Killing Fields, Geometric Symmetries and Black Hole Mergers