On noncommutative spherically symmetric spaces

Abstract

Two families of noncommutative extensions are given of a general space-time metric with spherical symmetry, both based on the matrix truncation of the functions on the sphere of symmetry. The first family uses the truncation to foliate space as an infinite set of spheres, and it is of dimension four and necessarily time-dependent; the second can be time-dependent or static, is of dimension five, and uses the truncation to foliate the internal space.

Noncommutative de Sitter and FRW spaces

“…To see whether this formalism can indeed describe noncommutative gravity we proceed by examples which fulfil previously mentioned requirements and have a certain relevance in physics. We discussed in previous papers [8,9,10] various rotationally invariant noncommutative spaces. In this paper we give examples of algebras with spherical symmetry which can be considered as fuzzy versions of cosmological metrics: de Sitter and…”

“…Following this approach we have made in our previous papers a survey of noncommutative algebras generated by four, five and six elements, [8,9,10]. The original motivation was in part to use interior derivatives, thereby decreasing the dimension of phase space.…”

“…We wish here to generalize the frame Ansatz and the constraints of [8] in order to obtain noncommutative cosmological spacetimes of the Friedmann-Robertson-Walker type. Let us briefly introduce the notation and write down the equations; for all technical details we refer to [8] as calculations are to some extent analogous. Coordinates are denoted by…”

Fuzzy de Sitter Space from kappa‐Minkowski Space in Matrix Basis

“…Whenever derivatives span a Lie algebra, the matrix algebra can be viewed as a quantization of the algebra of functions on a certain homogeneous space. Then, in principle, a quantization map can be defined explicitly, which might be particularly beneficial in an attempt to formulate quantized/non‐commutative counterparts of models used in cosmology or field theory on a curved background . Therefore, understanding of the quantization map associated to the κ‐Minkowski space in terms of matrix geometry is welcome.…”

Hydrogen atom in rotationally invariant noncommutative space

“…Much attention has also been received to studying of spherically symmetric noncommutative spaces [31][32][33], considering of the problem of violation of the Lorentz invariance (see for example [34][35][36]). For instance, noncommutative gauge theory without Lorentz violation was proposed in [34].…”