Generalising the coupling between spacetime and matter

TL;DR

This paper proposes a new fundamental tensor to describe a more complex matter-spacetime coupling, which can explain dark phenomena and resolve compatibility issues in alternative gravity theories.

Contribution

It introduces a generalized coupling tensor in Einstein's equations, extending the standard model to account for dark matter effects and improve compatibility in conformal gravity.

Findings

The new tensor can explain dark phenomenology within General Relativity.

The approach maintains compatibility with Newtonian gravity in the weak field limit.

It resolves compatibility issues in conformal gravity models.

Abstract

We explore the idea that the coupling between matter and spacetime is more complex than the one originally envisioned by Einstein. We propose that such coupling takes the form of a new fundamental tensor in the Einstein field equations. We then show that the introduction of this tensor can account for dark phenomenology in General Relativity, maintaining a weak field limit compatible with standard Newtonian gravitation. The same paradigm can be applied any other theory of gravitation. We show, as an example, that in the context of conformal gravity a generalised coupling is able to solve compatibility issues between the matter and the gravitational sector.