Tomaschitz, R. (1993). Electromagnetic radiation in multiply connected Robertson-Walker cosmologies, Journal of Mathematical Physics 34, 3133-3150, DOI: 10.1063/1.530067
Abstract (AIP, CDS, SAO/NASA ADS, Zbl 0811.53081)
Maxwell’s equations on a topologically nontrivial cosmological background are studied. The cosmology is locally determined by a Robertson–Walker line element, but the spacelike slices are open hyperbolic manifolds, whose topology and geometry may vary in time. In this context the spectral resolution of Maxwell’s equations in terms of horospherical elementary waves generated at infinity of hyperbolic space is given. The wave fronts are orthogonal to bundles of unstable geodesic rays, and the eikonal of geometric optics appears just as the phase of the horospherical waves. This fact is used to attach to the unstable geodesic rays a quantum mechanical momentum. In doing so the quantized energy-momentum tensor of the radiation field is constructed in a geometrically and dynamically transparent way, without appealing to the intricacies of the second quantization. In particular Planck’s radiation formula, and the bearing of the multiply connected topology on the fluctuations in the temperature of the background radiation is discussed.
WAVE FRONT, MAXWELL EQUATIONS, COSMOLOGICAL MODELS, TOPOLOGY, ELECTROMAGNETIC FIELDS, WAVE PROPAGATION, GEODESICS, ENERGY−MOMENTUM TENSOR, BACKGROUND RADIATION, PLANCK RADIATION FORMULA, SPACE−TIME, METRICS
98.80.Jk
Mathematical and relativistic aspects of cosmology
03.65.Ta
Foundations of quantum mechanics; measurement theory
05.45.-a
Nonlinear dynamics and chaos
Zbl
0811.53081
Tomaschitz, Roman
Electromagnetic radiation in multiply connected Robertson-Walker cosmologies
[J] J.
Math. Phys. 34, No.7, 3133-3150 (1993). ISSN 0022-2488
MSC 2000:
*53Z05
Appl. of differential geometry to physics
83C50 Electromagnetic fields
Keywords: spectral resolution; Maxwell's equations; elementary waves; hyperbolic space; Planck's radiation formula
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Electromagnetic radiation in multiply connected Robertson-Walker cosmologies |
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Tomaschitz, Roman |
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Journal of Mathematical Physics, Volume 34, Issue 7, July 1993, pp.3133-3150 |
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07/1993 |
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description: Roman Tomaschitz (1993) Electromagnetic radiation in multiply connected Robertson-Walker cosmologies, Journal of Mathematical Physics 34, 3133.
Keywords: open Robertson–Walker cosmology, multiply connected hyperbolic 3-space, Maxwell’s equations on hyperbolic 3-manifolds, geometrical optics, ray optics, unstable geodesic rays, eikonal equation, spectral resolution of electromagnetic fields on open hyperbolic 3-manifolds, energy–momentum tensor of the quantized radiation field, Planck distribution, temperature anisotropy of the cosmic microwave background radiation, global metrical deformations of the open 3-space, horospherical wave fronts, Poisson kernel, vectorial point-pair invariants, automorphic vector fields, Möbius transformations in the Poincaré half-space, universal covering space, fractal limit sets of Kleinian covering groups, Schottky groups, quasi-Fuchsian groups, Hausdorff dimension, discrete subgroups of the Lorentz group, fibered hyperbolic 3-manifolds, Poincaré series, Eisenstein series
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