Bound of Noncommutativity Parameter Based on Black Hole Entropy

Abstract

We study the bound of the noncommutativity parameter in the noncommutative Schwarzschild black hole which is a solution of the noncommutative ISO(3,1) Poincare gauge group. The statistical entropy satisfying the area law in the brick wall method yields a cutoff relation which depends on the noncommutativity parameter. Requiring both the cutoff parameter and the noncommutativity parameter to be real, the noncommutativity parameter can be shown to be bounded as $\Theta >8.4times10^{-2}{l}_p$.

LaTeX 7 pages, references added, minor corrections

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• Properties of an axisymmetric Lorentzian non-commutative black hole
• Non-commutative effects on gravitational measurements
• Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity
• Quantum Entanglement of Fermions- Antifermions Pair Creation modes in Non-commutative Bianchi I Space-time