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We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term ($ n> 3$) that is the generalization of three-dimensional local translations. This symmetry is obtained through the direct application of the converse of Noether's second theorem on the theory under consideration. We show that diffeomorphisms can be expressed as linear combinations of it and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action. As a result, the new internal symmetry together with local Lorentz transformations can be adopted as the fundamental gauge symmetries of general relativity. Although their gauge algebra is open in general, it allows us to recover, without resorting to the equations of motion, the very well-known Lie algebra satisfied by translations and Lorentz transformations in three …
IOP Publishing
Publication date: 
19 Sep 2017

Merced Montesinos, Diego González, Mariano Celada, Bogar Díaz

Biblio References: 
Volume: 34 Issue: 20 Pages: 205002
Classical and Quantum Gravity