Star products on extended massive non-rotating BTZ black holes

Details Star products on extended massive non-rotating BTZ black holes Star products on extended massive non-rotating BTZ black holes

2004-03-25

arxiv.org/abs/hep-th/0403257v1

JHEP 0406 (2004) 031

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 1 figure

Scientific paper

10.1088/1126-6708/2004/06/031

$AdS_3$ space-time admits a foliation by two-dimensional twisted conjugacy classes, stable under the identification subgroup yielding the non-rotating massive BTZ black hole. Each leaf constitutes a classical solution of the space-time Dirac-Born-Infeld action, describing an open D-string in $AdS_3$ or a D-string winding around the black hole. We first describe two nonequivalent maximal extensions of the non-rotating massive BTZ space-time and observe that in one of them, each D-string worldsheet admits an action of a two-parameter subgroup ($\ca \cn$) of $\SL$. We then construct non-formal, $\ca \cn$-invariant, star products that deform the classical algebra of functions on the D-string worldsheets and on their embedding space-times. We end by giving the first elements towards the definition of a Connes spectral triple on non-commutative $AdS$ space-times.

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