Deformed General Relativity and Torsion

TL;DR

This paper explores how deformed special relativity can be integrated into curved spacetime using a torsion-based extension of Einstein-Cartan theory, highlighting potential observable effects and clarifying misconceptions about noncommutative spacetime.

Contribution

It proposes a framework linking DSR to Einstein-Cartan theory with torsion, offering new insights into noncommutative translations without requiring fundamentally noncommutative spacetime.

Findings

Torsion may cause observable charge conservation violations on a 10^3 s timescale.

Noncommutative translations in Snyder algebra do not necessarily imply noncommutative spacetime.

The framework clarifies the relationship between DSR, torsion, and noncommutative geometry.

Abstract

We argue that the natural framework for embedding the ideas of deformed, or doubly, special relativity (DSR) into a curved spacetime is a generalisation of Einstein-Cartan theory, considered by Stelle and West. Instead of interpreting the noncommuting "spacetime coordinates" of the Snyder algebra as endowing spacetime with a fundamentally noncommutative structure, we are led to consider a connection with torsion in this framework. This may lead to the usual ambiguities in minimal coupling. We note that observable violations of charge conservation induced by torsion should happen on a time scale of 10^3 s, which seems to rule out these modifications as a serious theory. Our considerations show, however, that the noncommutativity of translations in the Snyder algebra need not correspond to noncommutative spacetime in the usual sense.