Spacetime Symmetries and Kepler's Third Law

Details Spacetime Symmetries and Kepler's Third Law Spacetime Symmetries and Kepler's Third Law

2012-02-13

arxiv.org/abs/1202.2893v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 3 figures

Scientific paper

In general relativity, the generators of symmetries are called Killing vector fields. The spacetime geometry of a system of two point masses moving on a circular orbit has a helical Killing vector (HKV). We show how Kepler's third law for circular orbits, and its generalization in post-Newtonian theory, can be recovered from a simple, covariant condition on the norm of that HKV. This unusual derivation can be used to illustrate some concepts of prime importance in a general relativity course, including those of Killing vector, covariance, coordinate dependence, and gravitational redshift.

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