Deformed General Relativity and Torsion

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.

20 pages, 1 figure, revtex; expanded sections 3 and 4 for clarity, moved material to appendix B, corrected a few minor errors

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• MacDowell-Mansouri gravity and Cartan geometry
• Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
• Lifting General Relativity to Observer Space
• Spontaneously broken Lorentz symmetry for Hamiltonian gravity
• Cartan geometry of spacetimes with a nonconstant cosmological function $\Lambda$
• Non-relativistic Matrix Inflation