Miguel BezaresPALOMERA QUIROZ, GONZALOGONZALOPALOMERA QUIROZDaniel J. PonsEnrique G. Reyes2023-01-052023-01-052015https://investigadores.udd.cl/handle/123456789/463710.1142/S02198878155003462-s2.0-84928585533WOS:000350752900009<jats:p> 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). </jats:p>geodesic motiondominant energy conditionaveraged dominant energy condition(3+1)-spacetime decompositionThe Ehlers–Geroch theorem on geodesic motion in general relativityResource Types::text::journal::journal article