Spacetime Symmetries and Kepler's Third Law - INSPIRE

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Spacetime Symmetries and Kepler's Third Law

Alexandre Le Tiec
(
- Maryland U.
)

Feb, 2012

11 pages

Published in:

Class.Quant.Grav. 29 (2012) 217002

e-Print:

1202.2893 [gr-qc]

DOI:

10.1088/0264-9381/29/21/217002

View in:

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Abstract: (arXiv)

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.

Note:

11 pages, 3 figures; minor changes and text improvements; matches version to appear in Class. Quant. Grav

vector: Killing
symmetry: space-time
gravitation: redshift
field theory: vector
space-time: geometry
general relativity
covariance
orbit
curvature
gravitation: weak field

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