An impediment to torsion from spectral geometry

TL;DR

This paper uses spectral geometry methods to argue that torsion should be excluded from physically acceptable gravity models because the spectral formulation of the Einstein tensor cannot be extended to include torsion.

Contribution

It introduces a spectral geometry-based argument demonstrating the incompatibility of torsion with the spectral formulation of gravity.

Findings

Spectral geometry cannot be extended to include torsion in the Einstein tensor.

Torsion is likely incompatible with the spectral approach to gravity.

The work provides a new perspective on the role of torsion in gravitational theories.

Abstract

Modifications of standard general relativity that bring torsion into a game have a long-standing history. However, no convincing arguments exist for or against its presence in physically acceptable gravity models. In this Letter, we provide an argument based on spectral geometry (using methods of pseudo-differential calculus) that suggests that the torsion shall be excluded from the consideration. We demonstrate that there is no well-defined functional extending to the torsion-full case of the spectral formulation of the Einstein tensor.