Pierre Bieliavsky et al JHEP06(2004)031 doi:10.1088/1126-6708/2004/06/031
Star products on extended massive non-rotating BTZ black holes
Pierre Bieliavsky1, Stéphane Detournay2, Philippe Spindel2 and Marianne Rooman3
Show affiliations 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 (
) of SL(2,
). We then construct non-formal, -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.
- Keywords
- PACS
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04.70.Bw Classical black holes
- Subjects
- Dates
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Issue 06 (June 2004)
Received 25 March 2004, accepted for publication 16 June 2004
Published 30 June 2004
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Star products on extended massive non-rotating BTZ black holes
Pierre Bieliavsky et al JHEP06(2004)031
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