Equivalence Principle for Massive Bodies. II. Theory

Abstract

The acceleration of a massive body in an external field for general space-time geometrical gravitational theories is obtained. The condition on the metric is such that $\frac{{m}_{g}}{{m}_{i}}=1$ is obtained, and we reobtain the result that $\frac{{m}_{g}}{{m}_{i}}=1$ in Einstein's theory for massive objects with time-independent internal structure. But it is shown that a measurement of $\frac{{m}_{g}}{{m}_{i}}$ for astronomical bodies would measure space-time metric components which have not been measured in other gravitational experiments. In the scalar-tensor gravitational theory due to Brans and Dicke, it is shown that $\frac{{m}_{g}}{{m}_{i}}$ differs from 1 by a term of the order of the massive body's gravitational self-energy divided by its total energy.