Fuzzy and discrete black hole models

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