Generalized deviation equation and determination of the curvature in General Relativity
General Relativity and Quantum Cosmology
2016-03-01 v2 Earth and Planetary Astrophysics
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.
Keywords
Cite
@article{arxiv.1511.08465,
title = {Generalized deviation equation and determination of the curvature in General Relativity},
author = {Dirk Puetzfeld and Yuri N. Obukhov},
journal= {arXiv preprint arXiv:1511.08465},
year = {2016}
}
Comments
16 pages, 5 figures, RevTex format