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arXiv · hep-th/0403257

Star products on extended massive non-rotating BTZ black holes

Pierre Bieliavsky·Stéphane Detournay·Marianne Rooman·Philippe Spindel
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Abstract

$AdS_3$ 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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Pierre Bieliavsky, Stéphane Detournay, Marianne Rooman, Philippe Spindel. 2004-03-25. Star products on extended massive non-rotating BTZ black holes. https://doi.org/10.1088/1126-6708%2F2004%2F06%2F031

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