On the Hamiltonian analysis of non-linear massive gravity

TL;DR

This work presents a non-perturbative, auxiliary-field approach to the Hamiltonian analysis of non-linear massive gravity, specifically addressing the Boulware-Deser ghost in dRGT models. By introducing auxiliary fields $\Phi^{\mu}_{\;\nu}$, the potential is rewritten so the lapse enters linearly, enabling a clear chain of constraints that yields an extra, physical condition and precludes the sixth ghost degree of freedom. The method provides a simple, albeit non-constructive, route to understanding why ghost-freedom persists for arbitrary reference metrics and non-minimal potentials, and it generalizes to bigravity with appropriate adjustments. While not replacing the standard square-root-based analysis, this formalism offers insight into the constraint structure and highlights avenues for formal, auxiliary-field techniques in nonlinear stability and perturbation theory.

Abstract

In this paper we present a very simple and independent argument for the absence of the Boulware-Deser ghost in the recently proposed potentially ghost-free non-linear massive gravity. The limitation is that, in its simple form, the argument is, in a sense, non-constructive and less explicit than the standard approach. However, the formalism developed here may prove to be useful for discussing the formal aspects of the theory.