Equivalence Principle for Massive Bodies Including Rotational Energy and Radiation Pressure

The Einstein gravitational theory and the Brans-Dicke gravitational theory are investigated for the gravitational-to-inertial mass ratio (m_gm_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 m_gm_i=1 for the massive systems. It is found that m_gm_i≠1 for a nonrotating star in the Brans-Dicke theory. The violation is of order 10^-6 for the Sun. In the Brans-Dicke theory there are also contributions to m_gm_i≠1 due to the radiation content of a star. This violation is of order (radiation energy)/(stellar mass), yielding a correction of about 10^-8 for the Sun.