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.