Quantum statistics and noncommutative black holes

Abstract

We study the behaviour of a scalar field coupled to a noncommutative black hole which is described by a $\kappa$-cylinder Hopf algebra. We introduce a new class of realizations of this algebra which has a smooth limit as the deformation parameter vanishes. The twisted flip operator is independent of the choice of realization within this class. We demonstrate that the $R$-matrix is quasi-triangular up to the first order in the deformation parameter. Our results indicate how a scalar field might behave in the vicinity of a black hole at the Planck scale.

8 pages, no figures, revtex4; in v2 some points are explained in more detail, few typos corrected and one reference added

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• Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
• Rainbow statistics
• Noncommutative Two Dimensional Gravities
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
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Cited by in corpus (18)

• On the $\kappa$-Dirac Oscillator revisited
• Geodesic equation in $k$-Minkowski spacetime
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Effects of Noncommutativity on the Black Hole Entropy
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• The 2D $\kappa$-Dirac oscillator
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Noncommutativity and logarithmic correction to the black hole entropy
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Differential forms and k-Minkowski spacetime from extended twist
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Involutive representations of coordinate algebras and quantum spaces
• Noncommutative correction to the entropy of charged BTZ black hole
• Conformal quantum mechanics and holography in noncommutative space-time
• Superdense star in a space-time with minimal length
• Phase structures in fuzzy geometries
• Entropy of black holes, charged probes and noncommutative generalization