Gravity from the viewpoint of theory of sources

TL;DR

This paper investigates the $G^2$-approximation of the Schwarzschild solution through the theory of sources, proposing a privileged coordinate system where the metric is directly sourced, revealing potential violations of Birkhoff's theorem.

Contribution

It introduces a source-based coordinate system for the Schwarzschild solution and analyzes the implications of source-generated terms in the metric.

Findings

The exterior metric includes a source-generated term resembling a gauge function.

This term is proportional to the matter ball's radius and may violate Birkhoff's theorem.

The approach aligns with Schwarzschild metric but emphasizes the physical observability of source effects.

Abstract

I examine the $G^2$-approximation of Schwarzschild solution from the viewpoint of theory of sources. The method suggests the following definition of the privileged coordinate system: it is a system in which in each approximation the gauge degrees of freedom are put to zero, i.e. the metric is formed solely by sources. I calculate the metric in this system. In $G^2$-approximation the exterior metric has the term which is of the form of a gauge function. Considering it as such I have the agreement with Schwarzschild metric. But I cannot consider it as a gauge function because it is generated by sources. It should be observable. It is proportional to the radius of matter ball and seems violate the Birckhoff theorem.