Fully Extended Quasi-Metric Gravity

TL;DR

This paper extends the quasi-metric gravity theory by adding an extra field equation, enabling the prediction of gravitational waves in vacuum while maintaining consistency with Newtonian limits.

Contribution

It introduces an extended quasi-metric gravity framework that allows gravitational waves without full coupling to stress-energy, aligning with general relativity in weak fields.

Findings

Predicts gravitational waves in vacuum similar to GR

Retains original results for static systems and cosmology

Maintains experimental consistency with original theory

Abstract

The original theory of quasi-metric gravity, admitting only a partial coupling between space-time geometry and the active stress-energy tensor, is too restricted to allow the existence of gravitational waves in vacuum. Therefore, said theory can at best be regarded as a wave-less approximation theory. However, the requirement that the weak-field limit of the contracted Bianchi identities should be consistent with the Newtonian limit of the local conservation laws, forbids a full coupling between space-time geometry and the active stress-energy tensor. Nevertheless, in this paper it is shown how it is possible to relax the restrictions on quasi-metric space-time geometry sufficiently to avoid these problems. That is, the original quasi-metric field equations can be extended with one extra field equation, without having said full coupling and such that the contracted Bianchi identities have a sensible Newtonian limit. For weak fields in vacuum, said extra field equation has a dynamical structure somewhat similar to that of its counterpart in canonical general relativity (GR). In this way, the prediction of weak GR-like gravitational waves in vacuum becomes possible. Moreover, exact results from the original quasi-metric gravitational theory are recovered for metrically static systems and for isotropic cosmology. This means that the current experimental status of the extended quasi-metric gravitational theory is the same as for the original theory, except for the prediction of weak GR-like gravitational waves in vacuum.