A proposal for a reduced phase space for time symmetric, Lorentzian gravity

TL;DR

This paper introduces a full gauge-fixing of the phase space in 4D Lorentzian General Relativity with time symmetry, using CDJ variables, leading to a unique analytic solution for initial value constraints.

Contribution

It provides a novel gauge-fixing approach that simplifies the phase space of GR, ensuring a unique solution to the initial value problem in the time symmetric case.

Findings

Existence of a unique analytic solution to initial constraints.

Four free functions per spacetime point in the reduced phase space.

Progress towards solving the reduced phase space problem of GR.

Abstract

In this paper we perform a full gauge-fixing of the phase space of four dimensional General Relativity (GR) of Lorentzian signature for the time symmetric case, using the CDJ variables. In particular, the Gauss' law constraint in the chosen gauge meets the conditions of the Cauchy-Kovalevskaya theorem for first order, quasilinear PDEs. This implies the existence of a unique analytic solution to the initial value constraints problem in some region of 3-space, featuring four free functions per spacetime point. This result constitutes a step toward addressal of the reduced phase space problem of GR.