Unimodular gravity with external sources

TL;DR

This paper shows that unimodular gravity, which restricts sources to traceless energy-momentum tensors, still predicts the same free energy as general relativity, matching all weak field experimental results.

Contribution

It demonstrates that unimodular gravity with external sources reproduces general relativity's predictions for free energy despite its different source restrictions.

Findings

Free energy matches general relativity for all sources

Unimodular gravity is consistent with weak field tests

Sources are limited to traceless energy-momentum tensors

Abstract

The only allowed source of the gravitational field in the unimodular theory, invariant under area-preserving (transverse) diffeomorphisms as well as Weyl transformations, is just the traceless piece of the energy-momentum tensor. This fact notwithstanding, the free energy produced by arbitrary sources (not only static ones) is identical to the one predicted by general relativity. This encompasses all weak field tests of gravitation.