Boundary dynamics and the statistical mechanics of the 2+1-dimensional black hole

Citation
M. Banados et al., Boundary dynamics and the statistical mechanics of the 2+1-dimensional black hole, NUCL PHYS B, 545(1-3), 1999, pp. 340-370
Citations number
40
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
NUCLEAR PHYSICS B
ISSN journal
0550-3213 → ACNP
Volume
545
Issue
1-3
Year of publication
1999
Pages
340 - 370
Database
ISI
SICI code
0550-3213(19990419)545:1-3<340:BDATSM>2.0.ZU;2-I
Abstract
We calculate the density of states of the 2 + 1-dimensional BTZ black hole in the micro- and grand-canonical ensembles. Our starting point is the rela tion between 2 + 1-dimensional quantum gravity and quantised Chem-Simons th eory. In the micro-canonical ensemble, we find the Bekenstein-Hawking entro py by relating a Kac-Moody algebra of global gauge charges to a Virasoro al gebra with a classical central charge via a twisted Sugawara construction. This construction is valid at all values of the black hole radius. At infin ity it gives the asymptotic isometries of the black hole, and at the horizo n it gives an explicit form for a set of deformations of the horizon whose algebra is the same Virasoro algebra. In the grand-canonical ensemble we de fine the partition function by using a surface term at infinity that is com patible with fixing the temperature and angular velocity of the black hole. We then compute the partition function directly in a boundary Wess-Zumino- Witten theory, and find that we obtain the correct result only after we inc lude a source term at the horizon that induces a non-trivial spin-structure on the WZW partition function, (C) 1999 Published by Elsevier Science B.V.