Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes
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A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $Λ$ 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.
14 pages, final version, to appear in Classical and Quantum Gravity
14 pages, final version, to appear in Classical and Quantum Gravity