Rastall gravity is equivalent to Einstein gravity

TL;DR

Rastall gravity, often viewed as a modified theory, is shown to be mathematically equivalent to Einstein's general relativity, with no fundamental differences in their gravitational descriptions.

Contribution

The paper demonstrates that Rastall gravity is mathematically equivalent to Einstein gravity, clarifying misconceptions about its novelty as a modified gravity theory.

Findings

Rastall gravity is equivalent to Einstein gravity.

The stress-energy tensor in Rastall gravity corresponds to a part of the conserved stress-energy.

No new physics beyond Einstein's general relativity is introduced.

Abstract

Rastall gravity, originally developed in 1972, is currently undergoing a significant surge in popularity. Rastall gravity purports to be a modified theory of gravity, with a non-conserved stress-energy tensor, and an unusual non-minimal coupling between matter and geometry, the Rastall stress-energy satisfying nabla_b [T_R]^{ab} = {\lambda/4} g^{ab} nabla_b R. Unfortunately, a deeper look shows that Rastall gravity is completely equivalent to Einstein gravity --- usual general relativity. The gravity sector is completely standard, based as usual on the Einstein tensor, while in the matter sector Rastall's stress-energy tensor corresponds to an artificially isolated part of the physical conserved stress-energy.