Gravity according to theory of sources

TL;DR

This paper derives an approximate exterior metric for a spherically symmetric ideal liquid ball using the theory of sources in the $G^2$-approximation, suggesting that measurements outside can determine the ball's radius.

Contribution

It introduces a method to obtain the exterior metric of a spherical liquid ball in the $G^2$-approximation using the theory of sources, linking external measurements to the ball's radius.

Findings

Exterior metric depends on the radius in $G^2$ terms

Measurement outside can infer the ball's radius

Uses integral equations of the theory of sources

Abstract

The metric of spherically symmetric ball of ideal liquid is considered in $G^2$- approximation with the help of theory of sources. Using the integral equations of this theory gives the exterior metric depending upon the radius of the ball of matter in some terms proportional to $G^2$..I argue that according this metric from measurement outside the ball one can infer the value of ball radius.