Constraint analysis of Fierz–Pauli action through linearization of its nonlinear action constraints

Abstract

In this research, by linearizing the constraints of massive gravity action, we obtain the constraints of Fierz–Pauli action and compare it with the constraints obtained from Hamiltonian analysis. We claim that the linearized form of gravity is the same as the Fierz–Pauli action. Its constraints are the linearized form of nonlinear action constraints. We will also compare about bigravity. Also, by linearizing the generating functional and gauge transformations of the Hilbert–Einstein action, we reach their linearized massless Fierz–Pauli form.