Exact Black Hole Solutions in Noncommutative Gravity

Abstract

An exact spherically symmetric black hole solution of a recently proposed noncommutative gravity theory based on star products and twists is constructed. This is the first nontrivial exact solution of that theory. The resulting noncommutative black hole quite naturally exhibits holographic behavior; outside the horizon it has a fuzzy shell-like structure, inside the horizon it has a noncommutative de Sitter geometry. The star product and twist contain Killing vectors and act non-trivially on tensors except the metric, which is central in the algebra. The method used can be applied whenever there are enough spacetime symmetries. This includes noncommutative versions of rotating and charged black holes and higher-dimensional and cosmological solutions.

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• Schwarzschild Geometry Emerging from Matrix Models
• Quantum tunneling and spectroscopy of noncommutative inspired Kerr black hole
• Field Theory on Curved Noncommutative Spacetimes
• Involutive representations of coordinate algebras and quantum spaces
• Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
• Tensor calculus on noncommutative spaces
• Non-commutative Einstein equations and Seiberg-Witten map
• Noncommutative Solitons of Gravity
• Emergent Abelian Gauge Fields from Noncommutative Gravity
• Spacetime Noncommutativity in Models with Warped Extradimensions
• Phase structures in fuzzy geometries
• Dirac Operators on Noncommutative Curved Spacetimes
• Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity
• Entropy of black holes, charged probes and noncommutative generalization
• Einstein Equations for a Noncommutative Spacetime of Lie-Algebraic Type
• Charge Enhancement of Noncommutative Gravity