Vladimir O. Soloviev, Margarita V. Tchichikina
The Hamiltonian formalism of bigravity and bimetric theories is constructed for the general form of potential between two metrics. It is natural to study the role played by the lapse and shift functions in theories with two metrics on the base of Kuchar's approach because then they do not depend on the choice of space-time coordinate frame. The algebra of first class constraints is derived in Dirac brackets constructed from the second class constraints. It is the celebrated algebra of the hypersurface deformations. Fixing one of the metrics we obtain a bimetric theory without any first class constrains. Then we can use the symmetries of the background metric to construct conserved quantities looking ultralocally when written through the potential. The special case of potential providing the less number for degrees of freedom will be treated in the companion paper.
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http://arxiv.org/abs/1211.6530
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