Theoretical Frameworks for Testing Relativistic Gravity. II. Parametrized Post-Newtonian Hydrodynamics, and the Nordtvedt Effect
Chandrasekhar's post-Newtonian equations of hydrodynamics are generalized to encompass any metric theory of gravity by the use of arbitrary metric parameters. The resultant Parametrized Post- Newtonian (PPN) hydrodynamical equations are then used to calculate the Newtonian acceleration of the center of mass of a massive body of perfect fluid toward a very distant point mass. This acceleration can be written in terms of a gravitational-mass tensor and the gradient of the Newtonian potential: maa - ma U. . The gravitational-mass tensor ma is equal to the isotropic inertial mass ( , plus a small correction ("Nordtvedt effect"), which depends on the gravitational internal energy of the body and on the metric parameters that characterize the particular theory being used. In general relativity, the gravitational mass is precisely equal to the inertial mass (correction terms vanish),in accordance with the equivalence principle. In Brans-Dicke theory the two masses differ by a small isotropic correction which varies from body to body, in violation of the equivalence principle. A simple explanation of these two results is discussed. This work generalizes and substantially agrees with previous calculations by Nordtvedt.