Characteristic equations of linearized $\lambda R$ gravity

A detailed Hamilton-Jacobi analysis for linearized $\lambda R$ gravity is developed. The model is constructed by rewriting linearized gravity in terms of a parameter $\lambda$ and new variables. The set of all hamiltonians is identified successfully, and the fundamental differential is established. The non-involutive hamiltonians are eliminated, and the Hamilton-Jacobi generalized brackets are calculated. Such brackets are used to report the characteristic equations, and the counting of the number of degrees of freedom is performed. We fixed the gauge to indicate an intimate closeness between the model under study and linearized gravity.