Abstract |
: |
[eng] This note is based on a talk given by one of the authors (S. D.) at the
"Rencontres Mathématiques de Glanon", held in Glanon in July 2004. We will
first introduce the BTZ black hole, solution of Einstein's gravity in 2+1
dimensions, and emphasize some remarkable properties of its geometry. We will
essentially pay attention to the non-rotating black hole, whose structure is
significantly different to the generic case. We will then turn the some aspects
of string theory, namely the emergence of non-commutative geometry and the
embedding of the BTZ black hole as an exact string background using the
Wess-Zumino-Witten (WZW) model. We will show the existence of winding symmetric
WZW D1-branes in this space-time from the geometrical properties of the
non-rotating black hole. Finally, we will introduce strict deformations of
these spaces, yielding an example of non-commutative lorentzian non-compact
space, with non-trivial causal structure.
Comment: 22pp, 16pp text, 10 figures, to appear in the prooceedings of the
"Rencontres mathématiques de Glanon", July 2004 |