Bezares, MiguelPalomera, GonzaloPons, Daniel J.Reyes, Enrique G.2016-01-282016-01-282015International Journal of Geometric Methods in Modern Physics, 2015, vol. 12, n° 03, 19 p.http://hdl.handle.net/11447/213http://dx.doi.org/10.1142/S0219887815500346We 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).en-USGeodesic motiondominant energy conditionaveraged dominant energy condition(3 + 1)-spacetime decompositionArtículo