Deriving Entangled Relativity

TL;DR

Entangled Relativity is a non-linear reformulation of Einstein's theory that recovers General Relativity in certain limits and is derived from a broader class of $f(R,\Lambda)$ theories, emphasizing matter-geometry coupling.

Contribution

The paper derives Entangled Relativity from $f(R,\Lambda)$ theories by a key condition, expanding the understanding of matter-geometry interactions in gravitational theories.

Findings

Entangled Relativity recovers GR solutions in the weak matter density limit.

Vacuum solutions of GR are limits of Entangled Relativity solutions as matter tends to zero.

Introduces a broader class of theories with intrinsic decoupling, not always matching GR solutions.

Abstract

Entangled Relativity is a non-linear reformulation of Einstein's theory that cannot be defined in the absence of matter fields. It recovers General Relativity without a cosmological constant in the weak matter density limit or whenever $\Lm = T$ on-shell, and it is also more parsimonious in terms of fundamental constants and units. In this paper, we show that Entangled Relativity can be derived from a general $f(R,\Lm)$ theory by imposing a single requirement: the theory must admit all solutions of General Relativity without a cosmological constant whenever $\Lm = T \neq 0$ on-shell, though not necessarily only those solutions. An important consequence is that all vacuum solutions of General Relativity without a cosmological constant are limits of solutions of Entangled Relativity when the matter fields tend to zero. In addition, we introduce a broader class of theories featuring an \textit{intrinsic decoupling}, which, however, do not generally admit the solutions of General Relativity.