On the absence of the Boulware-Deser ghost in novel graviton kinetic terms

TL;DR

This paper demonstrates that certain novel nonlinear graviton kinetic terms in bi-gravity models can be constructed to be free of the Boulware-Deser ghost by analyzing their Hamiltonian structure using the ADM formalism.

Contribution

It introduces a new class of bi-gravity models with nonlinear kinetic terms and proves their ghost-free nature through Hamiltonian analysis.

Findings

Hamiltonian analysis confirms absence of BD ghost

Additional constraints eliminate ghost degrees of freedom

Models are structurally similar to known ghost-free bi-gravity theories

Abstract

Using novel nonlinear kinetic terms for gravitons, a large class of bi-gravity models were constructed, which are potentially free of the Boulware-Deser (BD) ghost. In this work, we derive their Hamiltonians using the ADM formalism, and verify that the BD ghost is eliminated by additional constraints. The general Hamiltonian structure is analogous to that of the other class of bi-gravity models free of the BD ghost.