Fluctuation of Dirac operator and equivalence principle

TL;DR

This paper explores how fluctuations of the Dirac operator in noncommutative geometry can generate curvature and torsion, providing a novel perspective on the equivalence principle in general relativity.

Contribution

It introduces a fluctuation method for the Dirac operator in noncommutative geometry to derive gravitational effects from flat space.

Findings

Curvature and torsion can be generated from flat space via Dirac operator fluctuations

The method is demonstrated on two specific examples

Provides a new approach to understanding gravity in noncommutative geometry

Abstract

General Relativity formulated with Noncommutative geometry allows one to obtain, via the fluctuation of Dirac operator, an exact equivalence principle: generation of curvature and torsion from flat space. The fluctuation method presented in this report is applied on two examples.