On two pictures in the heuristic approach to gravity

TL;DR

This paper extends the heuristic approach to gravity beyond linear approximation, explores two conceptual pictures for understanding gravitation, and suggests modifications to general relativity, including a variable gravitational constant and a privileged isotropic frame.

Contribution

It introduces an extended heuristic framework for gravity that accommodates modifications of General Relativity and clarifies the role of gauge invariance and privileged frames.

Findings

The privileged system for constant gravitational fields is isotropic.

Gauge invariance may be unnecessary; focus on nonphysical degrees of freedom.

Gravitational constant may depend on the gravitational field.

Abstract

We examine the heuristic approach to constant gravitational field by Dehnen, H\"onl and Westpfahl, extending it everywhere beyond linear approximation. Then it becomes flexible to accommodate possible modifications of General Relativity. We have found that two pictures introduced in the related paper by Thirring are helpful in better understanding some features of gravitation. In particular, this approach suggest that the privileged system for constant gravitational field must be the isotropic one and that the requirement of gauge invariance in gravitation theory may be a luxury; it is sufficient to take care that the nonphysical degrees of freedom do not invalidate calculations. It follows from this approach that gravitational constant should depend on gravitational field and some universality in the form of metric of an asymmetric body is suggested.