Geodesic
Bigravity in the Kuchar̆ Hamiltonian formalism: The general case
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 3, pp. 393-407 Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop the Hamiltonian formalism of bigravity and bimetric theories for the general form of the interaction potential of two metrics. When studying the role of lapse and shift functions in theories with two metrics, we naturally use the Kuchar̆ formalism in which these functions are independent of the choice of the space–time coordinate system. We find conditions on the potential necessary and sufficient for the existence of four first-class constraints. These constraints realize a well-known hypersurface deformation algebra in the framework of the formalism of Dirac brackets constructed on the base of all second-class constraints. Fixing one of the metrics, we obtain a bimetric theory not containing first-class constraints. Conserved quantities corresponding to symmetries of the background metric can then be expressed ultralocally in terms of the metric interaction potential.
Keywords: bigravity, bimetric theory, massive gravity, Hamiltonian formalism, gravity theory. 
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V. O. Soloviev; M. V. Chichikina. Bigravity in the Kuchar̆ Hamiltonian formalism: The general case. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 3, pp. 393-407. http://geodesic.mathdoc.fr/item/TMF_2013_176_3_a4/

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