Superselection Sectors in Asymptotic Quantization of Gravity

TL;DR

This paper explores the structure of the space of gravitational radiation solutions at null infinity, revealing a fibered phase space with superselection sectors relevant for quantum gravity.

Contribution

It introduces a fibered phase space structure based on the scalar $ extPsi_2$ at null infinity and identifies superselection sectors in asymptotic quantum gravity.

Findings

Reduced phase space can be used as the space of quantum gravitons.

Superselection sectors arise due to the lack of a natural scalar product correspondence.

The structure is globally defined, independent of null infinity orientation.

Abstract

Using the continuity of the scalar $\Psi_2$ (the mass aspect) at null infinity through $i_o$ we show that the space of radiative solutions of general relativity can be thought of a fibered space where the value of $\Psi_2$ at $i_o$ plays the role of the base space. We also show that the restriction of the available symplectic form to each ``fiber'' is degenerate. By finding the orbit manifold of this degenerate direction we obtain the reduced phase space for the radiation data. This reduced phase space posses a global structure, i.e., it does not distinguishes between future or past null infinity. Thus, it can be used as the space of quantum gravitons. Moreover, a Hilbert space can be constructed on each ``fiber'' if an appropriate definition of scalar product is provided. Since there is no natural correspondence between the Hilbert spaces of different foliations they define superselection sectors on the space of asymptotic quantum states.