Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes

Abstract

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.

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

References in corpus (7)

• A Gravity Theory on Noncommutative Spaces
• Noncommutative geometry inspired charged black holes
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
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Cited by in corpus (1)

• Effective Polymer Dynamics of D-Dimensional Black Hole Interiors