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  • 1
    Electronic Resource
    Electronic Resource
    Special conformal Killing vector space-times and symmetry inheritance (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2616-2625 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Viscous heat-conducting fluid and anisotropic fluid space-times admitting a special conformal Killing vector (SCKV) are studied and some general theorems concerning the inheritance of the symmetry associated with the SCKV are proved. In particular, for viscous fluid space-times it is shown that (i) if the SCKV maps fluid flow lines into fluid flow lines, then all physical components of the energy-momentum tensor inherit the SCKV symmetry; or (ii) if the Lie derivative along a SCKV of the shear viscosity term ησab is zero then, again, we have symmetry inheritance. All space-times admitting a SCKV and satisfying the dominant energy condition are found. Apart from the vacuum pp-wave solutions, which are the only vacuum solutions that can admit a SCKV, the energy-momentum tensor associated with these space-times is shown to admit at least one null eigenvector and can represent either a viscous fluid with heat conduction or an anisotropic fluid. No perfect fluid space-times can admit a SCKV. These SCKV space-times and, also, space-times admitting a homothetic vector are used to illustrate the symmetry inheritance theorems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528492
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  • 2
    Electronic Resource
    Electronic Resource
    Qualitative analysis of a class of Bianchi V imperfect fluid cosmologies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1772-1779 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It has been shown that by utilizing a set of "dimensionless'' equations of state, the Einstein field equations governing Bianchi V imperfect fluid cosmologies reduce to a plane-autonomous system of equations. This plane-autonomous system shall be investigated here, and the qualitative behavior of the underlying cosmological models shall thereby be obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529654
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  • 3
    Electronic Resource
    Electronic Resource
    Space-times admitting special affine conformal vectors (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 649-652 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Space-times admitting a special affine conformal vector (SACV) are shown to be precisely the space-times that admit a special conformal Killing vector. All possible SACV space-times are listed together with the corresponding SACV's and covariantly constant tensors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528899
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  • 4
    Electronic Resource
    Electronic Resource
    Two-fluid cosmological models (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 406-416 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Homogeneous and isotropic, relativistic two-fluid cosmological models are investigated. In these models two separate fluids act as the source of the gravitational field, as represented by the FRW line element. The general theory of two-fluid FRW models in which neither fluid need be comoving or perfect is developed. However, attention is focused on the physically interesting special class of flat FRW models in which one fluid is a comoving radiative perfect fluid and the second a noncomoving imperfect fluid. The first fluid is taken to model the cosmic microwave background and the second to model the observed material content of the universe. One of the motivations of the present work is to model the observed velocity of our galaxy relative to the cosmic microwave background that was recently discovered by G. F. Smoot, M. V. Gorenstein, and R. A. Muller [Phys. Rev. Lett. 39, 898 (1977)]. Several models within this special class are found and analyzed. The models obtained are theoretically satisfactory in that they are represented by solutions of Einstein's field equations and the laws of thermodynamics in which all the physical quantities occurring in the solutions are suitably well behaved. In addition, the models are in agreement with current observations. Consequently it is believed that the models obtained are physically acceptable models of the universe.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527347
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  • 5
    Electronic Resource
    Electronic Resource
    Qualitative analysis of diagonal Bianchi type V imperfect fluid cosmological models (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4117-4144 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Einstein field equations for diagonal Bianchi type V imperfect fluid cosmological models with both viscosity and heat conduction are set up as an autonomous system of differential equations using dimensionless variables and a set of dimensionless equations of state. Models with and without a cosmological constant, λ, are investigated using the techniques from dynamical systems theory. It is shown that all models that satisfy the weak energy conditions isotropize. The introduction of viscosity (in particular) allows for a variety of different qualitative behaviors (including, for example, models with a negative deceleration parameter). Exact solutions that correspond to the singular points of the dynamical system are found. It is shown that the past asymptotic states are represented by self-similar cosmological models and, if λ=0, the future asymptotic states are also, in general, represented by self-similar cosmological models; in the exceptional cases the late time asymptotic state is represented by a de Sitter model with constant expansion, as is the case for solutions with λ ≠ 0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530845
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  • 6
    Electronic Resource
    Electronic Resource
    Induced matter theory and embeddings in Riemann flat space–times (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 361-373 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A class of five-dimensional space-times that contain four-dimensional hypersurfaces whose intrinsic metrics are of cosmological interest is investigated. First, the five-dimensional space–time is assumed to be Riemann flat—the problem of determining the intrinsic metrics of the four-dimensional hypersurfaces then becomes a problem of embedding in flat space–time. Second, the Riemann flat solutions are used as a starting point to find solutions to Einstein's vacuum field equations in five dimensions that are not Riemann flat. In particular, a new general class of five-dimensional vacuum solutions is found. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531395
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  • 7
    Electronic Resource
    Electronic Resource
    Homogeneous scalar field cosmologies with an exponential potential (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5256-5271 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We shall study spatially homogeneous cosmological models containing a self-interacting scalar field with an exponential potential of the form V(φ)=Λekφ. The asymptotic properties of these models are discussed. In particular, their possible isotropization and inflation are investigated for all values of the parameter k. A particular class of models is analyzed qualitatively using the theory of dynamical systems, illustrating the general asymptotic behavior. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532200
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  • 8
    Electronic Resource
    Electronic Resource
    Affine conformal vectors in space-time (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1754-1764 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: All space-times admitting a proper affine conformal vector (ACV) are found. By using a theorem of Hall and da Costa, it is shown that such space-times either (i) admit a covariantly constant vector (timelike, spacelike, or null) and the ACV is the sum of a proper affine vector and a conformal Killing vector or (ii) the space-time is 2+2 decomposable, in which case it is shown that no ACV can exist (unless the space-time decomposes further). Furthermore, it is proved that all space-times admitting an ACV and a null covariantly constant vector (which are necessarily generalized pp-wave space-times) must have Ricci tensor of Segré type {2,(1,1)}. It follows that, among space-times admitting proper ACV, the Einstein static universe is the only perfect fluid space-time, there are no non-null Einstein–Maxwell space-times, and only the pp-wave space-times are representative of null Einstein–Maxwell solutions. Otherwise, the space-times can represent anisotropic fluids and viscous heat-conducting fluids, but only with restricted equations of state in each case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529652
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  • 9
    Electronic Resource
    Electronic Resource
    FRW Models as Exact Viscous Magnetohydrodynamical Cosmologies (1984)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 422 (1984), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1984.tb23372.x
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  • 10
    Electronic Resource
    Electronic Resource
    Observations and FRW Models (1986)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 470 (1986), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1986.tb47994.x
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