Spherically symmetric non-commutative space: D=4

Abstract

In order to find a non-commutative analog of Schwarzschild or Schwarzschild-de Sitter black hole we investigate spherically symmetric spaces generated by four non-commutative coordinates in the frame formalism. We present two solutions which, however, do not possess the prescribed commutative limit. Our analysis indicates that the appropriate non-commutative space might be found as a subspace of a higher-dimensional space. © 2008 Springer-Verlag / Società Italiana di Fisica.