Einstein's "Prague field-equation" -- another perspective

TL;DR

This paper revisits Einstein's 1912 scalar gravity theory, highlighting its self-consistent energy sourcing and solutions resembling general relativity, offering pedagogical insights into flat-space gravity models.

Contribution

It demonstrates that Einstein's 1912 scalar field equation naturally arises from energy self-consistency and explores its solutions and relation to general relativity.

Findings

Solutions exhibit Buchdahl-like inequalities

The theory models star-like objects with GR-like features

Provides pedagogical insights into flat-space gravity models

Abstract

I reconsider Einstein's 1912 "Prague-Theory" of static gravity based on a scalar field obeying a non-linear field equation. I point out that this equation follows from the self-consistent implementation of the principle that all energies source the gravitational field according to E=m(c-squared). This makes it an interesting toy-model for the "flat-space approach" to General Relativity, as pioneered by Kraichnan and later Feynman. Solutions modelling stars show features familiar from GR, e.g., Buchdahl-like inequalities. The relation to full GR is also discussed. This lends this toy theory also some pedagogical significance.