arXiv subjects

Matthias Wollensak

Publications and source records attributed to Matthias Wollensak.

3 recordsLinked to original sources

arXiv2022

Weyl time evolution operator in planar Bianchi-type-I universes

In this paper, Dirac`s equation in anisotropic Bianchi-type-I background spacetimes is treated w.r.t. orthonormal frames. By specializing to the massless spinor case and metrics with power-law scale factors and planar symmetry, an analytical expression of the approximate time evolution operator is derived. By use of this operator, all approximate spinor solutions can be generated. By construction, these solutions agree asymptotically and at early times with the exact solutions. The operator approach is also well adapted for studying the case of small deviations from conformally flat backgrounds. In particular, it can be shown that the limiting case of vanishing anisotropy renders the correct

math-ph↗

arXiv2021

Massless Fermions in planar Bianchi type I universes: Exact and approximate solutions

Based upon the exact formal solutions of the Weyl-Dirac-equation in anisotropic planar Bianchi-type-I background spacetimes with power law scale factors, one can introduce suitable equivalence classes of the solutions of these models. The associated background spacetimes are characterized by two parameters. It is shown that the exact solutions of all models of a given equivalence class can be generated with the help of a special transformation of these two parameters, provided one knows a single exact solution of an arbitrary member of this class. The method can also be utilized to derive approximate solutions, i.e. solutions which exhibit the correct behavior at early and at late times as well. This is explicitly demonstrated for the case of the anisotropic Kasner background with axial symmetry.

hep-th↗

arXiv2018

Massless Fermions in anisotropic Bianchi type I spacetimes

The behavior of spin - 1/2 - particles in anisotropic Bianchi type I backgrounds is investigated utilizing the concept of differential forms and orthonormal frames. Specializing to the massless case and power law scale factors $α_j(t) = t^{q_j}$ of the metric where $q_1 = q_2 $, an analytical outcome for the time evolution operator in terms of Bessel functions is presented.

math-ph↗