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.

arXiv comment14 pages, final version, to appear in Classical and Quantum Gravity

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• Effective Polymer Dynamics of D-Dimensional Black Hole Interiors
• Geodesic equation in non-commutative gauge theory of gravity
• Field Theory on Curved Noncommutative Spacetimes
• Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
• Constructing noncommutative black holes
• Exact solutions of noncommutative vacuum Einstein field equations and plane-fronted gravitational waves
• Analogy between the Schwarzschild solution in a noncommutative gauge theory and the Reissner-Nordström metric
• Gravitational collapse of spherically symmetric stars in noncommutative general relativity
• Noncommutative Reissner-Nordstrøm Black hole
• Holographic Entanglement Entropy for noncommutative Anti-de Sitter space