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  • 1
    Electronic Resource
    Electronic Resource
    Kerr–Schild metrics revisited. II. The complete vacuum solution (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2448-2462 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The complete solution of Einstein's gravitational equations with a vacuum–vacuum Kerr–Schild pencil of metrics gab+Vlalb is obtained. Our result generalizes the solution of the Kerr–Schild problem with a flat metric gab (represented by the Kerr theorem) to the case when gab is the metric of a curved space-time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530516
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  • 2
    Electronic Resource
    Electronic Resource
    Solutions of the Regge equations on some triangulations of CP2 (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 2577-2586 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Simplicial geometries are collections of simplices making up a manifold together with an assignment of lengths to the edges that define a metric on that manifold. The simplicial analogs of the Einstein equations are the Regge equations. Solutions to these equations define the semiclassical approximation to simplicial approximations to a sum over geometries in quantum gravity. In this paper, we consider solutions to the Regge equations with a cosmological constant that give Euclidean metrics of high symmetry on a family of triangulations of CP2 presented by Banchoff and Kühnel. This family is characterized by a parameter p. The number of vertices grows larger with increasing p. We exhibit a solution of the Regge equations for p=2 but find no solutions for p=3. This example shows that merely increasing the number of vertices does not ensure a steady approach to a continuum geometry in the Regge calculus. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531958
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  • 3
    Electronic Resource
    Electronic Resource
    Kerr–Schild metrics revisited. I. The ground state (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2438-2447 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Kerr–Schild pencil of metrics gab+Λlalb is investigated in the generic case when it maps an arbitrary vacuum space-time with metric gab to a vacuum space-time. The theorem is proved that this generic case, with the field l shearing, does not contain the shear-free subclass as a smooth limit. It is shown that one of the Kóta–Perjés metrics is a solution in the shearing class.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530515
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  • 4
    Electronic Resource
    Electronic Resource
    Factor structure of the Tomimatsu–Sato metrics (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2197-2200 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the factoring property of the Tomimatsu–Sato metrics follows from the structure of special Hankel determinants. A set of linear algebraic equations determining the factors is found. The factors of the first five Tomimatsu–Sato metrics are tabulated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528545
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  • 5
    Electronic Resource
    Electronic Resource
    Classification of stationary space-times (1974)
    Springer
    International journal of theoretical physics 10 (1974), S. 217-227 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A systematic approach to the geometric structure of stationary gravitational fields is presented. The algebraic type of the trace-free Ricci tensor together with the propagation properties of the eigenrays in the background 3-space defined by the Killing trajectories serve as a basis for classifying the solutions of the stationary field equations. The eigenrays are the integral curves belonging to the solutions ξA of the eigenvalue problemG A B ξB=μξA,G A B spinor representing the gravitational field in the background space. Many of the already known stationary metrics can be derived in the present scheme but new solutions of the field equations are also obtained. The possible types of the vacuum and electrovac fields are discussed in their connection with the corresponding exact solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01811250
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  • 6
    Electronic Resource
    Electronic Resource
    Stationary vacuum fields with a conformally flat three-space. II. Proof of axial symmetry (1986)
    Springer
    General relativity and gravitation 18 (1986), S. 511-530 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The conjecture is proved that stationary vacuum space-times having a conformally flat three-space are axially symmetric. The proof uses the Ernst potential and the complex conjugate potential as independent coordinates. Two field equations: a combination of the Einstein equations and an integrability condition are algebraic in one of the field variables. Their coefficients, computed by employing a REDUCE program, separately vanish unless axial symmetry holds. Solution of the coefficient equations yields the proof of axial symmetry. Certain special classes of metrics must be excluded from the discussion. The axial symmetry of these exceptional classes has been proved in I.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00770466
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  • 7
    Electronic Resource
    Electronic Resource
    Canonical gravity in the parametric manifold picture (1994)
    Springer
    General relativity and gravitation 26 (1994), S. 759-779 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Canonical structures in the parametric picture of gravitation in general relativity are investigated. One of the fields, the scalarf, emerges as a secondary entity that interacts with a system consisting of the threemetricg and the connection formω. We are employing the (g,ω) system for developing a canonical approach. While a naïve attempt would appear to founder, we do find an extension of the phase-space of the system which is computationally viable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02105826
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  • 8
    Electronic Resource
    Electronic Resource
    Stationary vacuum fields with a conformally flat three-space. III. Complete solution (1986)
    Springer
    General relativity and gravitation 18 (1986), S. 531-547 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is shown that stationary vacuum space-times having a conformally flat 3-space are always characterized by a functional relationship between the real and imaginary parts of the Ernst potential. This result is based on a new formulation of Einstein's equation, and it completes the investigation of vacuum space-times with conformally flat spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00770467
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  • 9
    Electronic Resource
    Electronic Resource
    Petrov Types of Slowly Rotating Fluid Balls (2000)
    Springer
    General relativity and gravitation 32 (2000), S. 2319-2332 
    Details
    ISSN: 1572-9532
    Keywords: perfect fluid ; Petrov type ; slow rotation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are stated on the possible Petrov types of various fluid models. It is shown that Petrov type II solutions must reduce to the de Sitter spacetime in the static limit. Two space-times with a physically satisfactory energy-momentum tensor are investigated in detail. For the rotating incompressible fluid, it is proven that the Petrov type cannot be D. The equation of the rotation function ω can be solved for the Tolman type IV fluid in terms of quadratures. It is also shown that the rotating version of the Tolman IV space-time cannot be Petrov type D.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1001903726479
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  • 10
    Electronic Resource
    Electronic Resource
    Book review (1995)
    Springer
    General relativity and gravitation 27 (1995), S. 1011-1014 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02113083
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