The comoving coordinate frame for differentially rotating, relativistic bodies

A first-order, ordinary differential equation is derived that can in principle be integrated for any assumed rotation law Ω = Ω(r) within a relativistic, perfect-fluid body. The solution of this equation reduces the number of unknown metric functions appearing in the line element for the spacetime of such differentially rotating bodies to three. In the case of rigid rotation this is equivalent to a result of Harrison (Phys. Rev. D.; 1:2269 (1970)). (author)