Abstract
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 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
→
S
1
. We also study the 3D FLRW model on
R
×
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
×
S
3
Universe.
Funder
Consejo Nacional de Ciencia y Tecnología
Subject
Physics and Astronomy (miscellaneous)
Cited by
6 articles.
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1. Quantum Kaluza-Klein theory with M2(ℂ);Journal of High Energy Physics;2023-09-18
2. Quantum geodesic flows and curvature;Letters in Mathematical Physics;2023-06-22
3. Quantum Riemannian geometry of the discrete interval and q-deformation;Journal of Mathematical Physics;2023-05-01
4. Quantum geodesics on quantum Minkowski spacetime;Journal of Physics A: Mathematical and Theoretical;2022-10-21
5. Fuzzy Schwarzschild (2 + 1)-spacetime;Journal of Mathematical Physics;2022-08-01