Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-10-05
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages. Change in the title and wording of some sections to emphasize the main results. References added
Scientific paper
Though the Einstein's general relativity equations have been derived within the Einstein-Palatini formalism for an arbitrary connection, however the role of the connection not being the Levi Civita connection has not been understood clearly in all previous works. We clarify the whole situation by showing that the well known projective transformation relating the solution for the free connection and the Levi Civita connection is a gauge transformation and that the condition first introduced by Einstein for obtaining the Einstein equation of motion is nothing but a gauge fixing condition. The projective transformation has for the first time been realised and explicitly shown as a gauge symmetry. Further we also carry out a canonical analysis of constraints, degrees of freedom and find generators of the gauge symmetry. Thus we establish the full equivalence between the Einstein-Hilbert and the Einstein-Palatini formulations for an arbitrary free connection.
Dadhich Naresh
Pons Josep Maria
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