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  • 1
    Electronic Resource
    Electronic Resource
    Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups. I. Two Killing fields spanned on uα and wα (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 380-400 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Plebanski based on the Darboux theorem. In the resulting coordinates, the Killing vector fields (if any exist) assume a special form. Each Killing vector field may be either spanned on the fields of velocity and rotation or linearly independent of them. By considering all such cases one arrives at the classification. With respect to the structures of the groups, this is just the Bianchi classification, but with all possible orientations of the orbits taken into account. In this paper, which is part 1 of a 3-part series, all solutions are considered for which two Killing fields are spanned on velocity and rotation. The solutions of Lanczos and Gödel are identified as special cases, and their new invariant definitions are provided. In addition, a new invariant definition is given of the Ozsvath class III solution. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532300
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  • 2
    Electronic Resource
    Electronic Resource
    Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups. II. One Killing field spanned on uα and wα (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 401-422 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This is the second part of a series of 3 papers. Using the same method and the same coordinates as in part 1, rotating dust solutions of Einstein's equations are investigated that possess 3-dimensional symmetry groups, under the assumption that only one of the Killing fields is spanned on the fields of velocity uα and rotation wα, while the other two define vectors that are linearly independent of uα and wα at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations solved for the components of the metric tensor in every case that arises. The Einstein equations are simplified in a few cases, three (most probably) new solutions are found, and several classes of solutions known earlier are identified in the present scheme. They include those by Ozsváth, Maitra, Ellis, King, and Vishveshwara and Winicour. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532336
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  • 3
    Electronic Resource
    Electronic Resource
    Comment on "Space-times with plane-symmetric scalar waves'' [J. Math. Phys. 33, 3506 (1992)] (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 527-527 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530876
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  • 4
    Electronic Resource
    Electronic Resource
    Rotating Bianchi type V dust models generalizing the k=−1 Friedmann model (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 355-367 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Einstein equations are investigated for a rotating Bianchi type V dust model in which one of the Killing fields is spanned on velocity and rotation (case 1.2.2.2 in the classification scheme of the earlier papers). A first integral of the field equations is found, and with a special value of this integral coordinate transformations are used to eliminate two components of the metric. The k=−1 Friedmann model is shown to be contained among the solutions in the limit of zero rotation. The field equations for the simplified metric are reduced to 3 second-order ordinary differential equations that determine 3 metric components plus a first integral that algebraically determines the fourth component. First derivatives of the metric components are subject to a constraint (a second-degree polynomial with coefficients depending on the functions). It is shown that the set does not follow from a Lagrangian of the Hilbert type. The group of Lie point-symmetries of the set is found, it is two-dimensional noncommutative. Finally, a method of searching for first integrals (for sets of differential equations) that are polynomials of degree 1 or 2 in the first derivatives is applied. No such first integrals exist. The method is used to find a constraint (of degree 1 in first derivatives) that could be imposed on the metric, but it leads to a vacuum solution, and so is of no interest for cosmology. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1330197
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  • 5
    Electronic Resource
    Electronic Resource
    Friedmann limits of rotating hypersurface–homogeneous dust models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3628-3664 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The existence of Friedmann limits is systematically investigated for all the hypersurface–homogeneous rotating dust models, presented in previous papers by this author. Limiting transitions that involve a change of the Bianchi type are included. Except for stationary models that obviously do not allow it, the Friedmann limit expected for a given Bianchi type exists in all cases. Each of the three Friedmann models has parents in the rotating class; the k=+1 model has just one parent class, the other two each have several parent classes. The type IX class is the one investigated in 1951 by Gödel. For each model, the consecutive limits of zero rotation, zero tilt, zero shear, and spatial isotropy are explicitly calculated. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1378304
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  • 6
    Electronic Resource
    Electronic Resource
    Rotating dust solutions of Einstein's equations with three-dimensional symmetry groups. III. All Killing fields linearly independent of uα and wα (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2148-2179 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This is the third and last part of a series of three papers. Using the same method and the same coordinates as in papers I and II, rotating dust solutions of Einstein's equations are investigated that possess three-dimensional symmetry groups, under the assumption that each of the Killing vectors is linearly independent of velocity uα and rotation wα at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations are solved for the components of the metric tensor in every case that arises. No progress was made with the Einstein equations in any of the cases, and no previously known solutions were identified. A brief overview of literature on solutions with rotating sources is given. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532302
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  • 7
    Electronic Resource
    Electronic Resource
    On the thermodynamical interpretation of perfect fluid solutions of the Einstein equations with no symmetry (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 2602-2610 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Gibbs–Duhem equation dU+pdV=TdS imposes restrictions on the perfect fluid solutions of Einstein equations that have a one-dimensional symmetry group or no symmetry at all. In this paper, we investigate the restrictions imposed on the Stephani Universe and on the two classes of models found by Szafron. Upon the Stephani Universe and the β≠0 class of Szafron symmetries are forced. We find the most general subcases of the β=0 model of Szafron that are consistent with the Gibbs–Duhem equation and have no symmetry. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532000
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  • 8
    Electronic Resource
    Electronic Resource
    Shear-free normal cosmological models (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 433-441 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Shear-free normal cosmological models are the perfect fluid solutions of Einstein's equations in which rotation and shear vanish, and which are not static [they were all found by A. Barnes, Gen. Relativ. Gravit. 4, 105 (1973)]. They are either spherically, plane, or hyperbolically symmetric. Their symmetries are discussed in various coordinate systems and related to the conformal group of the three-dimensional flat space. A coordinate representation is introduced which unites all three cases into a single two-parameter family. The limiting transitions to the Friedman–Lemaitre–Robertson–Walker (FLRW) models and to the Schwarzschild–de Sitter-like solutions are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528462
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  • 9
    Electronic Resource
    Electronic Resource
    Editor's Note: Effect of Inhomogeneity on Cosmological Models, by Richard C. Tolman (1997)
    Springer
    General relativity and gravitation 29 (1997), S. 931-933 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018839401726
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  • 10
    Electronic Resource
    Electronic Resource
    Editor's Note (1999)
    Springer
    General relativity and gravitation 31 (1999), S. 115-117 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1016529506041
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