Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

Abstract

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{ö}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.

Latex2e file, 26 pages, no figures

References in corpus (11)

• Polymer Quantum Mechanics and its Continuum Limit
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Inflationary observables in loop quantum cosmology
• On the Possibility of Anisotropic Curvature in Cosmology
• Quantum FRW cosmological solutions in the presence of Chaplygin gas and perfect fluid
• Quantum integrability of quadratic Killing tensors
• Canonical Quantization of the BTZ Black Hole using Noether Symmetries
• Decoupling of the re-parametrization degree of freedom and a generalized probability in quantum cosmology
• Polymer quantization and Symmetries
• Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime
• Discrete spectrum of the quantum Reissner - Nordström geometry

Cited by in corpus (7)

• Crossing the phantom divide line as an effect of quantum transitions
• Bianchi type I, Schutz perfect fluid and evolutionary quantum cosmology
• Constructing the CKVs of Bianchi III and V spacetimes
• Classical and quantum analysis of 3D electromagnetic pp-wave spacetime
• Dynamically equivalent ΛCDM equations with underlying Bianchi Type geometry
• Quantum fate of timelike naked singularity with scalar hair
• Quantum Cosmology in $f(Q)$ theory