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Generalized deviation equation and determination of the curvature in General Relativity

We derive a generalized deviation equation -- analogous to the well-known geodesic deviation equation -- for test bodies in General Relativity. Our result encompasses and generalizes previous extensions of the standard geodesic deviation equation. We show how the standard as well as a generalized deviation equation can be used to measure the curvature of spacetime by means of a set of test bodies. In particular, we provide exact solutions for the curvature by using the standard deviation equation as well as its next order generalization.

preprint2016arXivOpen access
Dirk PuetzfeldYuri N. Obukhov
gr-qcastro-ph.EP
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Dirk PuetzfeldYuri N. Obukhov

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