TL;DR
This paper derives the constraint algebra in the Hamiltonian formalism of bigravity using a straightforward tetrad approach, clarifying the role of the Hassan-Rosen transform without relying on ansatz or implicit functions.
Contribution
It presents a direct derivation of the constraint algebra in bigravity via the tetrad Hamiltonian formalism, avoiding complex assumptions or Dirac brackets.
Findings
Constraint algebra derived explicitly in tetrad formalism
Hassan-Rosen transform interpreted as fixing a Lagrange multiplier
Comparison with other approaches provided
Abstract
The constraint algebra is derived in the second order tetrad Hamiltonian formalism of the bigravity. This is done by a straightforward calculation without involving any insights, implicit functions, and Dirac brackets. The tetrad approach is the only way to present the bigravity action as a linear functional of lapses and shifts, and the Hassan-Rosen transform (characterized as "a complicated redefinition of the shift variable" according to the authors) appears here not as an ansatz but as fixing of a Lagrange multiplier. A comparison of this approach with the other ones is provided.
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