Spherically Symmetric, Metrically Static, Isolated Systems in Quasi-Metric Gravity

Dag Østvang

Published 2002-01-31, updated 2018-11-28Version 7

The gravitational field exterior respectively interior to a spherically symmetric, isolated body made of perfect fluid is examined within the quasi-metric framework (QMF). It is required that the gravitational field is "metrically static", meaning that it is static except for the effects of the global cosmic expansion on the spatial geometry. Dynamical equations for the gravitational field are set up and an exact solution is found for the exterior part. Besides, equations of motion applying to inertial test particles moving in the exterior gravitational field are set up. By construction the gravitational field of the system is not static with respect to the cosmic expansion. This means that the radius of the source increases and that distances between circular orbits of inertial test particles increase according to the Hubble law. Moreover it is shown that if this model of an expanding gravitational field is taken to represent the gravitational field of the Sun (or isolated planetary systems), this has no serious consequences for observational aspects of planetary motion. On the contrary some observational facts of the Earth-Moon system are naturally explained within the QMF. Finally the QMF predicts different secular increases for two different gravitational coupling parameters. But such secular changes are neither present in the Newtonian limit of the quasi-metric equations of motion nor in the Newtonian limit of the quasi-metric field equations valid inside metrically static sources. Thus standard interpretations of space experiments testing the secular variation of G are explicitly theory-dependent and do not apply to the QMF.