부산대학교 도서관

After a careful discussion about just how difficult it is to define precisely what one means by equations of motion for extended bodies in general relativity, the authors present a generalized version of a theorem by P. S. Jang and the second author [J. Mathematical Phys. {\bf 16} (1975), 65--67; MR0356820 (50 \#9289)]. It is shown that, given a timelike curve $\gamma$ in a Lorentz manifold $(M,g)$ such that for any sufficiently small closed neighborhood $U$ there is a divergence-free symmetric tensor field $T_{ab}$ satisfying the dominant energy condition and vanishing on $\partial U$, and that this also holds true for all metrics in a $C^1[U]$-neighbourhood of $g$, then $\gamma$ is a geodesic (with respect to $g$).