1202.2893 (Alexandre Le Tiec)

Spacetime Symmetries and Kepler's Third Law    [PDF]

Alexandre Le Tiec

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.

View original: http://arxiv.org/abs/1202.2893