Non-commutative Corrections in Spectral Matrix Gravity

TL;DR

This paper investigates how non-commutative geometry modifies Einstein's equations by calculating first-order corrections and analyzing the spectral properties of a deformed gravitational theory.

Contribution

It introduces a novel non-commutative deformation of general relativity using spectral invariants and computes the initial corrections to Einstein's equations.

Findings

Derived first non-commutative corrections to Einstein equations

Analyzed the spectral properties of the deformed theory

Discussed related topics in non-commutative geometry and gravity

Abstract

We study a non-commutative deformation of general relativity based on spectral invariants of a partial differential operator acting on sections of a vector bundle over a smooth manifold. We compute the first non-commutative corrections to Einstein equations in the weak deformation limit and analyze the spectrum of the theory. Related topics are discussed as well.