Center of mass and far field metric in relativistic magnetohydrodynamics

The uniform motion of the center of mass of a charged, conducting fluid, in the presence of an electromagnetic field, is derived in the first post-Newtonian approximation of general relativity. Also the source's far field metric tensor is determined, and it is expressed in terms of parameters known as three-dimensional volume integrals over its interior. These results for the above system permit the physical identification, to post-Newtonian accuracy, of the integration constants and the coordinate systems involved in the Schwarzschild and the Kerr metric tensors.