Spherically Symmetric Noncommutative Space: d = 4

TL;DR

This paper explores noncommutative geometries with spherical symmetry to model black holes, presenting solutions that suggest higher-dimensional spaces may be necessary for accurate noncommutative analogs.

Contribution

It introduces two new spherically symmetric noncommutative space solutions and discusses the need for higher-dimensional frameworks for proper modeling.

Findings

Two noncommutative solutions without commutative limits

Indication that higher-dimensional spaces are needed

Potential pathway for noncommutative black hole models

Abstract

In order to find a noncommutative analog of Schwarzschild or Schhwarzschild-de Sitter blackhole we investigate spherically symmetric spaces generated by four noncommutative coordinates in the frame formalism. We present two solutions which however do not posess the prescribed commutative limit. Our analysis indicates that the appropriate noncommutative space might be found as a subspace of a higher-dimensional space.