On a weak Gauss law in general relativity and torsion

TL;DR

This paper demonstrates that the weak Gauss law in general relativity does not hold in Einstein-Cartan theory, suggesting torsion could potentially serve as an alternative explanation to dark matter.

Contribution

It provides an explicit example showing the failure of the weak Gauss law in Einstein-Cartan theory, highlighting torsion's possible role in cosmology.

Findings

Weak Gauss law fails in Einstein-Cartan theory

Torsion may replace dark matter

Explicit example illustrating the failure

Abstract

We present an explicit example showing that the weak Gauss law of general relativity (with cosmological constant) fails in Einstein-Cartan's theory. We take this as an indication that torsion might replace dark matter.