Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
| Autor: | Karagiorgos, A., Pailas, T., Dimakis, N., Terzis, Petros A., Christodoulakis, T. |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1475-7516/2018/03/030 |
| Popis: | We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor $F_{\mu\nu}$; the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor $T_{\mu\nu}$, suffice to reduce the general $F_{\mu\nu}$ to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{\"o}m one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free. Comment: Latex2e file, 26 pages, no figures |
| Databáze: | arXiv |
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