Vladimir O. Soloviev, Margarita V. Tchichikina
In the first part of this work (arXiv:1211.6530) it was shown that Hamiltonian formalism of bigravity with ultralocal potential of general form, under some conditions imposed on the potential, had 4 first class constraints, and their algebra was shown to be the algebra of hypersurface deformations. In this article we suppose that the potential in addition also satisfies a special degeneracy condition suggested by de Rham, Gabadadze, Tolley (dRGT), and calculate the constraint algebra of bigravity and massive gravity. In contrast to most works in this field, we do not use neither the explicit form of dRGT potential, nor the Hassan-Rosen transformation of variables, but follow some kind of axiomatic approach. Also we prefer Kuchar's Hamiltonian formulation, which involve embedding variables, to avoid a noncovariance. For bigravity we obtain 3 second class constraints, whereas one degree of freedom is included in the phase space in addition to 12 standard ones. Given the presence of 4 first class constraints, total number of gravitational degrees of freedom in bigravity occurs 7+1/2, and for massive gravity 5+1/2. This conclusion may occur wrong in case of one magic cancellation. We cannot exclude for sure this opportunity as we do not work with the genuine dRGT potential, but only with its substitute.
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http://arxiv.org/abs/1302.5096
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