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  • 1970-1974  (3)
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Material
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Qualitative magnetic cosmology (1972)
    Springer
    Communications in mathematical physics 27 (1972), S. 37-43 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The technique of phase plane analysis, which was used in a previous paper [4] to study the behaviour of a class of perfect-fluid anisotropic cosmological models, is applied to some simple anisotropic models that contain a uniform magnetic field. A formal correspondence is established between these magnetic models (of Bianchi type I) and certain perfect fluid models (of Bianchi type II), and new exact solutions are consequently discovered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01649657
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Tilting at cosmological singularities (1974)
    Springer
    Communications in mathematical physics 39 (1974), S. 131-151 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A detailed investigation is made of the simplest type of general relativistic perfect fluid cosmological models that possess a singularity at which all physical quantities are well-behaved. These models are spatially homogeneous, axisymmetric generalisations of the open (k/it=−1) Robertson-Walker universes. A pictorial description of the evolution of the models is obtained by using the qualitative theory of differential equations. The most surprising feature that emerges is that for some (non-empty) models the matter density may become zero, within a finite time, on a null hypersurface which acts as a Cauchy horizon for the models. This result is generalized to most other types of spatially homogeneous models. It is also discovered that the behaviour of the models varies dramatically with the type of matter content. This casts some doubts on the validity of assuming definite equations of state in general relativity, and suggests an investigation of the structural stability of Einstein's field equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01608392
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    More qualitative cosmology (1971)
    Springer
    Communications in mathematical physics 23 (1971), S. 137-158 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Standard geometric techniques of differential equation theory are employed to determine the qualitative behaviour of a set of non-rotating perfect-fluid cosmologies, whose spatially homogeneous hypersurfaces admit a 3-parameter group of isometries of Bianchi types I, II, III, V, or VI. In this way we are led to some new exact solutions of the field equations. The field equations for a broad class of cosmological models are presented in a regularised form, limitations on the use of this procedure are examined, and some suggestions are made of ways of avoiding the difficulties that arise.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01877756
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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