The Ehlers–Geroch theorem on geodesic motion in general relativity
Date
2015
Type:
Artículo
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Abstract
We provide a detailed and rigorous proof of (a generalized version of) the Ehlers–Geroch
theorem on geodesic motion in metric theories of gravity: we assume that (M, g) is a
spacetime satisfying an averaged form of the dominant energy condition and some further technical assumptions indicated in the bulk of this paper. Then, a small body which is allowed to deform the original spacetime metric g moves, nonetheless, along a geodesic of (M, g).
Description
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Citation
International Journal of Geometric Methods in Modern Physics, 2015, vol. 12, n° 03, 19 p.
Keywords
Geodesic motion, dominant energy condition, averaged dominant energy condition, (3 + 1)-spacetime decomposition