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  • 1
    Electronic Resource
    Electronic Resource
    Relativistic theory of spherically symmetric perturbation in dust universe (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2462-2465 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Starting from the initial value formulation of dust solution given in the preceding paper [J. Math. Phys. 31, 2459 (1990)] a relativistic perturbation equation and its general solutions in spherically symmetric universes are derived. It is found that these solutions are in analogy with the Bonnor–Weinberg results of the Newtonian theory and contain three modes: a growing mode, a decaying mode, and a constant mode.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528989
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  • 2
    Electronic Resource
    Electronic Resource
    Radiating sources in higher-dimensional gravity (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4963-4970 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study a time-dependent five-dimensional (5D) metric which contains a static four-dimensional (4D) sub-metric whose three-dimensional (3D) part is spherically symmetric. An expansion in the metric coefficient allow us to obtain close-to Schwarzschild approximation to a class of spherically symmetric solutions. Using Campbell's embedding theorem and the induced-matter formalism we obtain two 4D solutions. One describes a source with the stiff equation of state believed to be applicable to dense astrophysical objects, and the other describes a spherical source with a radial heat flow. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1401139
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  • 3
    Electronic Resource
    Electronic Resource
    Time-dependent Kaluza–Klein soliton solutions (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 4070-4079 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Time-dependent generalizations of the standard static, spherically symmetric solutions of the empty Kaluza–Klein or (4+1) Einstein equations are considered herein. Such time-dependent solutions exist because Birkhoff's theorem does not hold in (4+1) gravity. The solutions depend on the time and radius but not the fifth or internal coordinate, and fall into four classes with distinct mathematical properties. Physically, some of our solutions represent a static 4D space–time with an oscillating or contracting extra dimension, which suggests their relevance to particle physics. Others represent an expanding 3D space with a contracting extra dimension, which suggests their relevance to cosmology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530027
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  • 4
    Electronic Resource
    Electronic Resource
    Exact solutions of general relativity derived from 5-D "black hole'' solutions of Kaluza–Klein theory (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3888-3891 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the 5-D "black hole'' solutions of Kaluza–Klein theory can be reduced to new exact solutions of 4-D general relativity in which the matter is a spherically symmetric anisotropic fluid of radiation. This approach also provides new insights into the parameters and solutions of Kaluza–Klein theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529835
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  • 5
    Electronic Resource
    Electronic Resource
    Spherically symmetric density perturbation in relativistic cosmology (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2279-2282 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Einstein's field equations for spherically symmetric perfect fluids are reduced to two equations plus three definitions, and from these the spherical density perturbation equation is derived. It is found that this perturbation equation can be separated into two equations by the method of separation of variables and can be solved explicitly in some special cases. An interesting result is that for matter-dominated era the perturbation equation is found to be of the Bonnor form of Newtonian theory. Another interesting result is that for zero-curvature universe and radiation-dominated era the density perturbation has two growing modes: one is something like a power of the proper time, and the other is of the exponential law of the conformal time, each corresponds to a different limit of approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529509
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  • 6
    Electronic Resource
    Electronic Resource
    Cosmological models in globally geodesic coordinates. I. Metric (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1920-1923 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A thought method of measuring distances and recording times by using light signals and the observer's own clock is introduced into cosmological models of homogeneous and isotropic universes. From this a coordinate transformation that brings the Robertson–Walker metric into a new coordinate system is derived. It is found that this system is a globally geodesic coordinate system that reduces to a local inertial frame at the position of the observer who is moving freely with the cosmological fluid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527455
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  • 7
    Electronic Resource
    Electronic Resource
    Cosmological models in globally geodesic coordinates. II. Near-field approximation (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1924-1927 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A near-field approximation dealing with the cosmological field near a typical freely falling observer is developed within the framework established in the preceding paper [J. Math. Phys. 28, xxxx(1987)]. It is found that for the matter-dominated era the standard cosmological model of general relativity contains the Newtonian cosmological model, proposed by Zel'dovich, as its near-field approximation in the observer's globally geodesic coordinate system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527456
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  • 8
    Electronic Resource
    Electronic Resource
    Initial value formulation for the spherically symmetric dust solution (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2459-2461 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An initial value formulation for the dust solution with spherical symmetry is given explicitly in which the initial distributions of dust and its velocity on an initial surface are chosen to be the initial data. As special cases, the Friedmann universe, the Schwarzschild solution in comoving coordinates, and a spherically symmetric and radially inhomogeneous cosmological model are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528988
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  • 9
    Electronic Resource
    Electronic Resource
    A Class of Kaluza-Klein Solutions Curved in 4D and Flat in 5D (1998)
    Springer
    General relativity and gravitation 30 (1998), S. 509-514 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We give a broad class of solutions of the Kaluza-Klein equations that is static, spherically symmetric in 3D, curved in 4D and flat in 5D. These solutions generalize others that have been applied in cosmology and astrophysics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018819127980
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  • 10
    Electronic Resource
    Electronic Resource
    Five-dimensional Kaluza-Klein black holes coupled to massive scalar particles (1991)
    Springer
    General relativity and gravitation 23 (1991), S. 759-765 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Spherically symmetric solutions coupled to massive scalar particles in five-dimensional Kaluza-Klein theory are obtained. The solutions contain two event horizons. The inner horizon corresponds to the Schwarzschild black hole and the outer one is a new horizon which is produced by the massive scalar particles. It is found that the massive modes contribute an effective cosmological constant to the four-dimensional Einstein theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00755993
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