The principle of equivalence and projective structure in space-times

Details The principle of equivalence and projective structure in space-times The principle of equivalence and projective structure in space-times

2007-03-21

arxiv.org/abs/gr-qc/0703104v1

Class.Quant.Grav.24:3617-3636,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, submitted to Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/24/14/005

This paper discusses the extent to which one can determine the space-time metric from a knowledge of a certain subset of the (unparametrised) geodesics of its Levi-Civita connection, that is, from the experimental evidence of the equivalence principle. It is shown that, if the space-time concerned is known to be vacuum, then the Levi-Civita connection is uniquely determined and its associated metric is uniquely determined up to a choice of units of measurement, by the specification of these geodesics. It is further demonstrated that if two space-times share the same unparametrised geodesics and only one is assumed vacuum then their Levi-Civita connections are again equal (and so the other metric is also a vacuum metric) and the first result above is recovered.

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