Spacetime Symmetries and Kepler's Third Law
General Relativity and Quantum Cosmology
2013-08-26 v2
Abstract
The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a simple, covariant condition on the norm of the associated helical Killing vector field. This unusual derivation can be used to illustrate some concepts of prime importance in a general relativity course, including those of Killing field, covariance, coordinate dependence, and gravitational redshift.
Cite
@article{arxiv.1202.2893,
title = {Spacetime Symmetries and Kepler's Third Law},
author = {Alexandre Le Tiec},
journal= {arXiv preprint arXiv:1202.2893},
year = {2013}
}
Comments
11 pages, 3 figures; minor changes and text improvements; matches version to appear in Class. Quant. Grav