1. The concepts of COM and rest frame for a spatially extended relativistic system are somewhat subtle, and not uniquely defined. See Refs. 2 and 3.
2. A. Schild, inRelativity Theory and Astrophysics, 1. Relativity and Cosmology, Lectures in Applied Mathematics, Vol. 8, edited by J. Ehlers (Am. Math. Soc., Providence, RI, 1967), pp. 17–20.
3. H. P. Robertson and T. W. Noonan,Relativity and Cosmology(Saunders, Philadelphia, 1968), §5.4 and 5.5, pp. 139–144.
4. It will be seen below that this assumption involves no loss of generality.
5. We use Latin letters for spatial indices, and Greek for Minkowski indices. Our Minkowski metric shall be (l,−1,−1,−1), and we use the normal convention ɛ123 = −1, ɛijk = −ɛjik, and ɛijk = ɛjik.