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

TL;DR

This paper explores a quasi-metric gravity framework for spherically symmetric, isolated systems, deriving solutions and analyzing implications for planetary motion and cosmic expansion effects, with some observational consistency and novel predictions.

Contribution

It provides an exact exterior solution and equations of motion within the quasi-metric framework, highlighting how cosmic expansion influences gravitational fields and planetary systems.

Findings

The gravitational field expands with the universe, increasing distances between test particles.

The model explains certain Earth-Moon system observations naturally.

Different gravitational coupling parameters predict distinct secular changes.

Abstract

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.