The weaving of curved geometries

TL;DR

This paper introduces a method for constructing weave states in loop quantum gravity that represent non-flat geometries, including the Schwarzschild solution, expanding the applicability of weave states beyond flat spacetime.

Contribution

It presents a novel construction of weave states for non-flat geometries, specifically including the Schwarzschild solution, advancing the understanding of quantum states in curved spacetimes.

Findings

Weave states for non-flat geometries are successfully constructed.

The Schwarzschild solution is explicitly represented by a weave state.

This work extends the applicability of weave states in loop quantum gravity.

Abstract

In the physical interpretation of states in non-perturbative loop quantum gravity the so-called weave states play an important role. Until now only weaves representing flat geometries have been introduced explicitly. In this paper the construction of weaves for non-flat geometries is described; in particular, weaves representing the Schwarzschild solution are constructed.