Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes

Details Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes

2008-09-03

arxiv.org/abs/0809.0614v2

Class.Quant.Grav.26:085014,2009

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, final version, to appear in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/26/8/085014

A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $\Lambda$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The metrics and curvatures of the quantum Schwarzschild spacetime and the quantum Schwarzschild-de Sitter spacetime are computed. It is shown that up to the second order in the deformation parameter, the quantum spacetimes are solutions of a noncommutative Einstein equation which is proposed in this paper.

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