# Two Approaches to Hamiltonian Bigravity

## Abstract

**:**

## 1. Introduction

- potential can be explicitly expressed in canonical coordinates;
- it follows from standard constraint analysis that symmetry conditions for the pair of tetrads is not postulated;
- Hassan–Rosen transformation of variables also follows from constraints treatment according to the Dirac algorithm;
- coefficients in Poisson algebra of the key second-class constraint $\mathcal{S}$ are explicitly expressed through canonical coordinates.

## 2. Method of Implicit Functions

- different implicit functions are used; in the first case it is matrix ${D}_{\phantom{\rule{4pt}{0ex}}j}^{i}$, and in the second case it is the potential $\tilde{U}=U/N$;
- special transformation (14) is required in the first case;
- potential can be displayed almost explicitly, i.e., employing the implicit function ${D}_{\phantom{\rule{4pt}{0ex}}j}^{i}$, in the first case [21].

## 3. Method of Tetrads

#### 3.1. Tetrads in GR

#### 3.2. Choice of Tetrad Parametrization in Bigravity

#### 3.3. The Constraints of Tetrad Bigravity

#### 3.4. The Algebra of Constraints

## 4. Conclusions

## Funding

## Conflicts of Interest

## Appendix A

## Notes

1 | |

2 | It was shown for the first time in reference [49]. |

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Soloviev, V.O.
Two Approaches to Hamiltonian Bigravity. *Universe* **2022**, *8*, 119.
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Two Approaches to Hamiltonian Bigravity. *Universe*. 2022; 8(2):119.
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2022. "Two Approaches to Hamiltonian Bigravity" *Universe* 8, no. 2: 119.
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