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  • 1
    Electronic Resource
    Electronic Resource
    Solutions to wave equations on black hole geometries. II (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2286-2296 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Methods from the author's previous work and the classes of solutions which they produce are extended to the wave equations which govern the massive scalar field and the massless spin- 1/2 field on the Kerr–Newman geometry and the massless fields of spin 1 and 2 on the Kerr geometry. The solutions found are exact and expressed in simple closed forms in terms of elementary functions, but they only exist when appropriate constraints hold on some of the black hole parameters and on the frequency of the field in some cases. The behavior on the horizon, at null infinity, and with respect to the angular variables is analyzed for some example solutions. For the examples studied, it is found that the ones having radial behavior of a normal mode are not free of angular singularities. An exact relation is established between the scalar wave equation on the extreme Kerr–Newman geometry and the Whittaker–Hill equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526811
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  • 2
    Electronic Resource
    Electronic Resource
    Wake-free waves in one and three dimensions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 106-108 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A recent paper by Gottlieb [J. Math. Phys. 29, 2434 (1988)] provides examples of acoustic wave equations, in various dimensions, that have nontrivial families of solutions that are progressing waves of order 1, and relates this to whether or not these equations satisfy Huygens' principle. A statement made in that paper related to Huygens' principle in one space dimension is clarified, and it is shown in this connection that, in general, the relationship between the possession of progressing wave solutions and the satisfaction of Huygens' principle is more complex than the situation described by Gottlieb. In addition, the attractive properties of progressing waves of order 1 are retained by progressing waves of any finite order, and we use this to generalize in several ways Gottlieb's results on "wake-free'' solutions of the acoustic equation in three dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529132
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  • 3
    Electronic Resource
    Electronic Resource
    An approximation scheme for scalar waves in a Schwarzschild geometry (1978)
    Springer
    General relativity and gravitation 9 (1978), S. 1119-1128 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Schwarzschild geometry is approximated by a certain set of conformally flat shells. As an example of the use of this approximation, the transmission coefficientT for spherical waves of monochromatic scalar radiation imploding on the black hole is calculated by solving the scalar wave equation within each conformally flat space and matching across the interfaces. The results agree with those of other authors for low and high frequencies and give values ofT at all intermediate frequencies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00756578
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  • 4
    Electronic Resource
    Electronic Resource
    Progressing waves on spherical spacetimes (1988)
    Springer
    General relativity and gravitation 20 (1988), S. 343-358 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A family of spherically symmetrical spacetimes that are transparent to minimally coupled scalar multipole waves is investigated. The concept of transparency is reformulated in terms of the established concept of “progressing waves.” The set of spherically symmetric spacetimes and the family of wave equations for which the transparency condition can be shown to hold is generalized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00758959
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  • 5
    Electronic Resource
    Electronic Resource
    Note on Kantowski-Sachs spacetimes (1988)
    Springer
    General relativity and gravitation 20 (1988), S. 603-606 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is shown that a portion of de Sitter space can be expressed in the formds 2=dt 2−A 2 (t)dr 2−B 2(t)(dθ 2+sin 2 θdφ 2). It follows that it is a Kantowski-Sachs spacetime, according to the usual definition. This disproves the statement sometimes seen in the literature that all Kantowski-Sachs spacetimes are anisotropic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00758916
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  • 6
    Electronic Resource
    Electronic Resource
    Note on equivalence of cosmological space-times (1986)
    Springer
    General relativity and gravitation 18 (1986), S. 585-589 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is shown that only de Sitter space and Minkowski space can be expressed in more than one of the standard forms for Robertson-Walker space-times.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00769926
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  • 7
    Electronic Resource
    Electronic Resource
    Generalized Darboux maps and massless spin-s fields (1989)
    Springer
    General relativity and gravitation 21 (1989), S. 509-515 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider conformally invariant massless spin-s field equations on a spherically symmetrical space-time. Precisely when these equations are consistent appropriately defined field components are shown to satisfy wave equations related by a generalization of the classical Darboux map.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00904502
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  • 8
    Electronic Resource
    Electronic Resource
    Master equation for some gauge invariant gravitational perturbations (1990)
    Springer
    General relativity and gravitation 22 (1990), S. 1387-1396 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Gerlach and Sengupta derived a master equation for arbitrary odd-parity gravitational perturbations of spherically symmetrical space-times. In this paper we show that for radiative purely gravitational perturbations of Robertson-Walker space-times the same equation governs the evenparity perturbations as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00756837
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  • 9
    Electronic Resource
    Electronic Resource
    Progressing wave gravitational perturbations of Robertson-Walker space-times (1990)
    Springer
    General relativity and gravitation 22 (1990), S. 1397-1412 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In a series of papers Janis and coworkers found a family of Robertson-Walker space-times whose most general radiative purely gravitational perturbations could be expressed as progressing waves. In this paper we significantly generalize, simplify, and extend, their results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00756838
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  • 10
    Electronic Resource
    Electronic Resource
    Conformal invariance under spatial inversion of extreme Reissner-Nordström black holes (1984)
    Springer
    General relativity and gravitation 16 (1984), S. 789-792 
    Details
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The extreme Reissner-Nordström geometry is shown to be conformally invariant under a spatial inversion. Generalization of this result to other geometries is briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00762916
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