The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies. I. The Maclaurin spheroids and the virial theorem

Abstract

The post-Newtonian effects of general relativity on the equilibrium of uniformly rotating bodies are considered with the aid of a suitably generalized version of the classical tensor virial theorem. An exact relation exhibiting the relativistic effects is obtained; and it shows that, if the figure of equilibrium is approximated by a spheroid, the effect of general relativity is to attribute to the spheroid a larger angular velocity than the Newtonian value.