Equivalence Principle for Massive Bodies Including Rotational Energy and Radiation Pressure

Abstract

The Einstein gravitational theory and the Brans-Dicke gravitational theory are investigated for the gravitational-to-inertial mass ratio ($\frac{{m}_{g}}{{m}_{i}}$) they yield for massive systems. We examine models for stars in equilibrium but undergoing rotation or containing electromagnetic radiation. General conditions on the space-time metric of many mass sources are obtained which lead to $\frac{{m}_{g}}{{m}_{i}}=1$ for the massive systems. It is found that $\frac{{m}_{g}}{{m}_{i}}\ensuremath{\ne}1$ for a nonrotating star in the Brans-Dicke theory. The violation is of order ${10}^{\ensuremath{-}6}$ for the Sun. In the Brans-Dicke theory there are also contributions to $\frac{{m}_{g}}{{m}_{i}}\ensuremath{\ne}1$ due to the radiation content of a star. This violation is of order (radiation energy)/(stellar mass), yielding a correction of about ${10}^{\ensuremath{-}8}$ for the Sun.