Electromagnetic self-forces and generalized Killing fields

Abstract

Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own electromagnetic fields. New notions of effective linear and angular momenta are identified, and their evolution equations are derived exactly in arbitrary (but fixed) curved spacetimes. A slightly modified form of the Detweiler-Whiting axiom that a charge's motion should only be influenced by the so-called "regular" component of its self-field is shown to follow very easily. It is exact in some interesting cases, and approximate in most others. Explicit equations describing the center-of-mass motion, spin angular momentum, and changes in mass of a small charge are also derived in a particular limit. The chosen approximations -- although standard -- incorporate dipole and spin forces that do not appear in the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have, however, been previously identified in the test body limit.

20 pages, minor typos corrected

References in corpus (8)

• Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space
• Approximate spacetime symmetries and conservation laws
• Self-forces from generalized Killing fields
• Quadrupole effects on the motion of extended bodies in Kerr spacetime
• Quadrupole effects on the motion of extended bodies in Schwarzschild spacetime
• Equations of Motion in General Relativity of a Small Charged Black Hole
• Extended-body effects in cosmological spacetimes
• Dixon's extended bodies and impulsive gravitational waves

Cited by in corpus (24)

• The motion of point particles in curved spacetime
• Self-force and radiation reaction in general relativity
• Mechanics of extended masses in general relativity
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• Motion of small objects in curved spacetimes: An introduction to gravitational self-force
• High-order expansions of the Detweiler-Whiting singular field in Schwarzschild spacetime
• Bobbing and Kicks in Electromagnetism and Gravity
• Motion in classical field theories and the foundations of the self-force problem
• Spacetime dynamics of spinning particles - exact electromagnetic analogies
• Caustics and wave propagation in curved spacetimes
• A Tail of a Quark in N=4 SYM
• 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
• Generic effective source for scalar self-force calculations
• Self-force: Computational Strategies
• Regularization of static self-forces
• Effective stress-energy tensors, self-force, and broken symmetry
• Self-forces on static bodies in arbitrary dimensions
• Self-forces in arbitrary dimensions
• Foundations of the self-force problem in arbitrary dimensions
• Motion of localized sources in general relativity: gravitational self-force from quasilocal conservation laws
• Static Self-Forces in a Five-Dimensional Black Hole Spacetime
• Regularization of a scalar charged particle for generic orbits in Kerr spacetime
• Self-force and the Schwarzschild star