On some global problems in the tetrad approach to quasi-local quantities
| Autor: | Szabados, Laszlo B |
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| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Class.Quant.Grav.25:195004,2008 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/0264-9381/25/19/195004 |
| Popis: | The potential global topological obstructions to the tetrad approach to finding the quasi-local conserved quantities, associated with closed, orientable spacelike 2-surfaces S, are investigated. First we show that the Lorentz frame bundle is always globally trivializable over an open neighbourhood U of any such S if an open neighbourhood of S is space and time orientable, and hence a globally trivializable SL(2,C) spin frame bundle can also be introduced over U. Then it is shown that all the spin frames belonging to the same spinor structure on S have always the same homotopy class. On the other hand, on a 2-surface with genus g, there are $2^{2g}$ homotopically different Lorentz frame fields, and there is a natural one-to-one correspondence between these homotopy classes and the different SL(2,C) spinor structures. Comment: 13 pages, a more detailed discussion of the problems is given, Theorems 3.1 and 3.2 are modified slightly, the proof of Theorem 4.3 is improved, 5 references are added, misprints are corrected. Appearing in Class. Quantum Grav |
| Databáze: | arXiv |
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