Star products on extended massive non-rotating BTZ black holes
arXiv:hep-th/0403257 · doi:10.1088/1126-6708/2004/06/031
Abstract
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 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 space-times.
arXiv comment25 pages, 1 figure
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