Geodesically equivalent metrics in general relativity |
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Authors: | Vladimir S Matveev |
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Institution: | Institute of Mathematics, FSU Jena, 07737 Jena, Germany |
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Abstract: | We discuss whether it is possible to reconstruct a metric from its nonparameterized geodesics, and how to do it effectively. We explain why this problem is interesting for general relativity. We show how to understand whether all curves from a sufficiently big family are nonparameterized geodesics of a certain affine connection, and how to reconstruct algorithmically a generic 4-dimensional metric from its nonparameterized geodesics. The algorithm works most effectively if the metric is Ricci-flat. We also prove that almost every metric does not allow nontrivial geodesic equivalence, and construct all pairs of 4-dimensional geodesically equivalent metrics of Lorentz signature. |
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Keywords: | Nonparameterized geodesics Geodesically equivalent metrics Affine connections General relativity |
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