Mathematics – Logic
Scientific paper
Mar 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phdt........16f&link_type=abstract
Thesis (PhD). UNIVERSITY OF CINCINNATI, Source DAI-B 61/03, p. 1467, Sep 2000, 147 pages.
Mathematics
Logic
Scientific paper
In this dissertation we study black hole space-time manifolds (BTZ black hole) in 2+1 dimensions. There are two objectives in this thesis. One is to investigate the modification of the BTZ black hole with charge. The other is to investigate the BTZ black hole from the Chern- Simons gauge theory point of view. In 2+1 dimensions, the logarithmic nature of the electromagnetic potential causes diverging masses to the solutions of Einstein-Maxwell theory. In order to cure these divergences, we included a Chern-Simons term as a topological mass to the photon in the action which screens the electromagnetic potential. We obtained solutions for self(anti) dual electromagnetic fields which were regular and asymptotic to the extreme BTZ black hole. In the Chern-Simons gauge theory approach, we couple sources to the Chern-Simons gauge theory as anti-de Sitter states specified by Casimir invariants of the anti-de Sitter group. We show how the relevant features of the black hole emerge by computing the flat connections of the gauge theory. Most importantly, treating the source as an unitary representation of the anti-de Sitter group leads to a discrete tower of excited states which provides a microscopic model for the black hole. By extending Chern-Simons gauge theory of gravity with N = 2 supersymmetry and coupling it to a supersource characterized by Casimir invariants of anti-de Sitter supergroup, we obtained a supermultiplet of black holes.
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