Noncommutative BTZ Black Hole in Polar Coordinates

Abstract

Based on the equivalence between the three dimensional gravity and the Chern-Simons theory, we obtain a noncommutative BTZ black hole solution as a solution of $U(1,1)\times U(1,1)$ noncommutative Chern-Simons theory using the Seiberg-Witten map. The Seiberg-Witten map is carried out in a noncommutative polar coordinates whose commutation relation is equivalent to the usual canonical commutation relation in the rectangular coordinates up to first order in the noncommutativity parameter $\theta$. The solution exhibits a characteristic of noncommutative polar coordinates in such a way that the apparent horizon and the Killing horizon coincide only in the non-rotating limit showing the effect of noncommutativity between the radial and angular coordinates.

14 pages, V2: minor changes, v3: reduced for clarification, a reference added

References in corpus (5)

• A Gravity Theory on Noncommutative Spaces
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• On Black Holes and Cosmological Constant in Noncommutative Gauge Theory of Gravity
• Deformed Reissner--Nordstrom solutions in noncommutative gravity
• Gauging the twisted Poincare symmetry as noncommutative theory of gravitation

Cited by in corpus (1)

• Noncommutative BTZ Black Hole in Different Coordinates