Generalized deviation equation and determination of the curvature in General Relativity

2015/11/30 by Dirk Puetzfeld, Yuri N. Obukhov · 1 citation
Physics and Astronomy · #astro-ph.EP #gr-qc

paper · pdf · doi:10.1103/physrevd.93.044073

published as Phys. Rev. D 93, 044073 (2016) · 16 pages, 5 figures, RevTex format

arxiv created 2016/02/29 · arxiv updated 2016/03/01

Abstract

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.

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