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Advanced General RelativityGravity Waves, Spinning Particles, and Black Holes$
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Claude Barrabès and Peter A. Hogan

Print publication date: 2013

Print ISBN-13: 9780199680696

Published to Oxford Scholarship Online: September 2013

DOI: 10.1093/acprof:oso/9780199680696.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 16 October 2021

Equations of motion

Equations of motion

(p.28) 3 Equations of motion
Advanced General Relativity
Oxford University Press

A technique for extracting the relativistic equations of motion of Schwarzschild, Reissner–Nordström, or Kerr particles moving in external fields, from the vacuum Einstein or Einstein–Maxwell field equations, as appropriate, is motivated and explained. The distinguishing features of the technique are (1) the use of a coordinate system attached to the null hypersurface histories of the wavefronts of the radiation produced by the particle motion, (2) the emergence of the approximate equations of motion of the particle from the field equations and the requirement that the wavefronts are smoothly deformed spheres near the particle, and (3) the absence of infinities arising in the process. The particular case of a spinning particle or Kerr particle is described in detail. The particles are not test particles although spinning test particles are also discussed.

Keywords:   Reissner–Nordström particle, Kerr particle, equations of motion, Schwarzschild particle, Einstein-Maxwell field equations, infinities, spinning particle

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