Some exact solutions of the Dirac equation in the Kasner space-time

Shishkin, G.V.; Андрушкевич, И. Е.

doi:10.1016/0375-9601(85)90324-x

Cited by 13 publications

(5 citation statements)

References 2 publications

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“…The special case a = 1 has been studied in Ref. [30]. The corresponding spacetime represents the planar (flat) Kasner solution with Kasner exponents (0, 0, 1).…”

Section: Exact Solutionsmentioning

confidence: 99%

Massless fermions in planar Bianchi-type-I universes: exact and approximate solutions

Wollensak

2021

Eur. Phys. J. C

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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.

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“…The special case a = 1 has been studied in Ref. [30]. The corresponding spacetime represents the planar (flat) Kasner solution with Kasner exponents (0, 0, 1).…”

Section: Exact Solutionsmentioning

confidence: 99%

Massless fermions in planar Bianchi-type-I universes: exact and approximate solutions

Wollensak

2021

Eur. Phys. J. C

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“…The Dirac equation in the flat Kasner-type space-time was considered by Shishkin and Andrushkevic [23] and Pimentel [24] with m = 0 .…”

Section: Dirac Equationmentioning

confidence: 99%

Particle Creation in some LRS Bianchi I models

Pimentel,

Pineda

2021

Preprint

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“…Every point (µ, ν) ∈ U represents a pBI universe described by spacetime (10). Due to (11) any equivalence class [ δ ] can be visualized in U as a straight line defined by ν(µ) = −δµ + 1. u a maps then a given point (µ, ν) lying on this straight line into a different point (aµ, ν(aµ)) being on the same line.…”

Section: Exact Solutionsmentioning

confidence: 99%

“…The special case a = 1 (flat Kasner background) has been studied in ref. [11]. For the class [ 0 ] one obtains the solutions:…”

Section: Exact Solutionsmentioning

confidence: 99%

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

Wollensak

2019

Preprint

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Based upon the exact formal solutions of models which obey the Weyl -Dirac -equation in planar Bianchi -type -I background spacetimes, one can introduce suitable equivalence classes of these models characterized by two parameters. It can be shown then that with the help of a special transformation of these parameters or, equivalently, of a related constrained coordinate transformation, the exact solutions of all models of a given equivalence class can be generated, provided one knows an exact solution of an arbitrary member of this equivalence class.This method also works if only approximate solutions are at disposal, which will be explicitly demonstrated in the case of the anisotropic Kasner spacetime with axial symmetry.

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Some exact solutions of the Dirac equation in the Kasner space-time

Cited by 13 publications

References 2 publications

Massless fermions in planar Bianchi-type-I universes: exact and approximate solutions

Massless fermions in planar Bianchi-type-I universes: exact and approximate solutions

Particle Creation in some LRS Bianchi I models

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

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