Dualized Gravity beyond Linear Approximation

TL;DR

This paper develops a loop space formalism for general relativity, introducing dual variables and curvature to explore gravitational monopoles and duality beyond linear approximation.

Contribution

It constructs a novel loop space duality framework for gravity that extends beyond linear approximation and connects to topological features like monopoles.

Findings

Loop space duality reduces to Hodge duality in linearized gravity.

Loop space curvature vanishes without topological defects.

A monopole charge for gravitational monopoles is proposed.

Abstract

We will construct a loop space formalism for general relativity, and construct the Polyakov variables as connections for such a loop space. We will use these Polyakov variables to construct a dual theory of gravity beyond linear approximation. It will be demonstrated that this loop space duality reduces to the Hodge duality for linearized gravity. Furthermore, a loop space curvature will be constructed from this Polyakov variable. It will be shown that this loop space curvature vanishes in the absence of topological defects, and so it can be used to investigate gravitational monopoles. We will also construct the suitable monopole charge for such gravitational monopoles.