Born-Type Rigid Motion in Relativity

Rigid motions of collections of particles as defined by Born, Herglotz, and Noether are studied in special and general relativity. An approximate method for solving the field equations of general relativity, the equations of motion of a perfect fluid undergoing a rigid motion, and the boundary condition $p=0\mathrm{}$ is described and the first-order solution for the first two sets of equations is obtained. It is shown that in the classical limit the boundary conditions may be satisfied to this order.