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

TL;DR

This paper explores nonlinear gravitons in 4-D general relativity by expanding around the Kodama state, resulting in a complex gravity theory with a well-defined quantum Hilbert space and preserved physical degrees of freedom.

Contribution

It introduces a new approach to realize nonlinear gravitons through fluctuations about the Kodama state, addressing issues of normalizability and Hilbert space structure.

Findings

Preservation of physical degrees of freedom under linearization

Construction of a Hilbert space of states annihilated by the quantum Hamiltonian constraint

Quantization of the theory at both linearized and nonlinear levels

Abstract

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.