Equations of Motion in General Relativity of a Small Charged Black Hole

Abstract

We present the details of a model in general relativity of a small charged black hole moving in an external gravitational and electromagnetic field. The importance of our model lies in the fact that we can derive the equations of motion of the black hole from the Einstein-Maxwell vacuum field equations without encountering infinities. The key assumptions which we base our results upon are that (a) the black hole is isolated and (b) near the black hole the wave fronts of the radiation generated by its motion are smoothly deformed spheres. The equations of motion which emerge fit the pattern of the original DeWitt and Brehme equations of motion (after they "renormalise"). Our calculations are carried out in a coordinate system in which the null hypersurface histories of the wave fronts can be specified in a simple way, with the result that we obtain a new explicit form, particular to our model, for the well-known "tail term" in the equations of motion.

arXiv comment31 pages, Latex file

References in corpus (13)

• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• The motion of point particles in curved spacetime
• Self-force via a Green's function decomposition
• A Rigorous Derivation of Gravitational Self-force
• Calculating the gravitational self force in Schwarzschild spacetime
• Self-force of a scalar field for circular orbits about a Schwarzschild black hole
• Gravitational self-force on a particle orbiting a Kerr black hole
• Computing the gravitational self-force on a compact object plunging into a Schwarzschild black hole
• Scalar, electromagnetic, and gravitational self-forces in weakly curved spacetimes
• Regularization parameters for the self force in Schwarzschild spacetime: II. gravitational and electromagnetic cases
• Regularization parameters for the self force in Schwarzschild spacetime: I. scalar case
• Covariant Self-force Regularization of a Particle Orbiting a Schwarzschild Black Hole - Mode Decomposition Regularization -

Cited by in corpus (10)

• The motion of point particles in curved spacetime
• Cosmic censorship in overcharging a Reissner-Nordström black hole via charged particle absorption
• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• Singular perturbation techniques in the gravitational self-force problem
• Motion of Small Bodies in Classical Field Theory
• Electromagnetic self-forces and generalized Killing fields
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• Motion of small bodies in general relativity: foundations and implementations of the self-force
• Equations of Motion of Schwarzschild, Reissner-Nordstrom and Kerr Particles
• Gravitational clock compass and the detection of gravitational waves