Fuzzy and discrete black hole models*

Abstract Using quantum Riemannian geometry, we solve for a Ricci = 0 static spherically-symmetric solution in 4D, with the S 2 at each t , r noncommutative fuzzy sphere, finding dimension jump solutions having time and radial form of classical 5D Tangherlini black hole. Thus, even small amount angular noncommutativity leads to radically different behaviour, modifying Laplacian weak gravity limit. We likewise provide version 3D hole 1 now discrete circle Z n inside 4D Schwarzschild far from horizon. study limit ${\mathbb{Z}}_{n}\to {S}^{1}$?> → S 1 . also FLRW model on $\mathbb{R}{\times}{S}^{2}$?> mathvariant="double-struck">R × 2 an expanding sphere find that Friedmann equation expansion is one closed $\mathbb{R}{\times}{S}^{3}$?> 3 Universe.