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arXiv · 0808.2330

Noncommutative BTZ Black Hole in Polar Coordinates

Ee Chang-Young·Daeho Lee·Youngone Lee
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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 $θ$. 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.

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Ee Chang-Young, Daeho Lee, Youngone Lee. 2008-12-15. Noncommutative BTZ Black Hole in Polar Coordinates. https://doi.org/10.1088/0264-9381%2F26%2F18%2F185001

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