Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions
In a preamble, a quick summary of the line of thought from Noether's theorems to modern views on conserved charges in gauge theories is attempted. Most of the background material needed for the thesis is set out through a small survey of the literature. Emphasis is put on the concepts more than...
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| Format: | Doctoral Thesis |
| Language: | fr |
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Universite Libre de Bruxelles
2007
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| Online Access: | https://dipot.ulb.ac.be/dspace/bitstream/2013/210694/1/3e5828e2-0887-4f39-b7c4-74f525d5108b.txt https://dipot.ulb.ac.be/dspace/bitstream/2013/210694/4/692edf16-16ac-4471-b8a5-faa5e4111c6d.txt http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210694 |
| Summary: | In a preamble, a quick summary of the line of thought from Noether's theorems to modern views on conserved charges in gauge theories is attempted. Most of the background material needed for the thesis is set out through a small survey of the literature. Emphasis is put on the concepts more than on the formalism, which is relegated to the appendices.<p><p>The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism.<p>The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described.<p><p><p>The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed. === Doctorat en Sciences === info:eu-repo/semantics/nonPublished |
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