Nonlinear gravitons in 4-D general relativity by expansion about the Kodama state

In this paper we provide a possible realization of Penrose's idea of nonlinear gravitons using a new description of nonmetric general relativity. In the addressal of issues surrounding the normalizability of the Kodama state and its reliability as a ground state for gravity, we expand the theory in fluctuations about the Kodama state. This produces a theory of complex gravity with a well-defined Hilbert space structure, whose quantization we carry out both at the linearized level and in the full nonlinear theory. The results of this paper demonstrate the preservation of the physical degrees of freedom of the full nonlinear theory under linearization, as well provide a Hilbert space of states of the former annihilated by the quantum Hamiltonian constraint.