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  • 1
    Electronic Resource
    Electronic Resource
    Jacobi's principle for magnetic interactions (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4903-4910 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the trajectories of a charged particle in a static magnetic field and a velocity-independent potential in a three-dimensional space are (the projection of) the geodesics of a suitably defined metric in a four-dimensional space. It is shown that each one-parameter group of isometries of the original configuration space that leaves the magnetic field invariant gives rise to a one-parameter group of isometries of the metric defined on the four-dimensional space and, hence, to a constant of the motion. It is also shown, similarly, that the Schrödinger equation for a charged particle in a static magnetic field is equivalent to the Schrödinger equation for a free particle in the four-dimensional space mentioned above. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533006
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  • 2
    Electronic Resource
    Electronic Resource
    Self-duality and gravitational perturbations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4099-4105 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that there exists a one-to-one correspondence between the real solutions of the Einstein vacuum field equations linearized about the Minkowski metric and the (complex) metric perturbations whose curvature to first order in the metric perturbation is self-dual. It is also shown that the self-duality condition of the curvature to first order in the metric perturbation is equivalent to a set of first-order equations for the metric perturbation whose solution is given by a scalar potential that obeys the wave equation. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532947
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  • 3
    Electronic Resource
    Electronic Resource
    Three-dimensional formulation of the Maxwell equations for stationary space–times (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2882-2890 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using the correspondence between a stationary space–time and a curved three-dimensional space with a static magnetic field and a conservative field of force, the Maxwell equations in a stationary space–time are expressed in terms of fields associated with the corresponding three-dimensional geometry. The Maxwell equations take a form analogous to the one they have in flat space–time. The Ricci tensor of the space–time is also written in terms of the three-dimensional fields. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532733
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  • 4
    Electronic Resource
    Electronic Resource
    Gravitational and electromagnetic perturbations of the Schwarzschild solution (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 5684-5694 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the complete metric and vector potential perturbations of the Schwarzschild solution can be expressed in terms of radial functions that share several differential properties. The energy flux of the incident, reflected, and absorbed gravitational and electromagnetic waves is given and the polarization changes are also analyzed. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531734
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  • 5
    Electronic Resource
    Electronic Resource
    Debye potentials and Hamiltonians for magnetic field line flow (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 3413-3418 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that any divergence-free vector field invariant under a group of volume-preserving transformations can be expressed locally in terms of two scalar potentials which depend on two variables only. It is also shown that the corresponding field line equations can be written in Hamiltonian form with one of these potentials as the Hamiltonian. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530969
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  • 6
    Electronic Resource
    Electronic Resource
    Spin-weighted cylindrical harmonics and the Euclidean group of the plane (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3856-3862 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the spin-weighted cylindrical harmonics s Jαm(ρ,φ), which are functions defined on the plane, are related to representation matrices of the group of rigid motions on the plane. It is also shown that the raising and lowering operators of the spin weight and of the z component of the angular momentum are related to two copies of the Lie algebra of the Euclidean group of the plane.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530011
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  • 7
    Electronic Resource
    Electronic Resource
    Debye potentials for Rarita–Schwinger fields in curved space-times (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 1323-1328 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Expressions for the complete solution of the Rarita–Schwinger equation in terms of complex scalar potentials are obtained by means of Wald's method of adjoint operators. The background space-time is required to be an algebraically special solution of the Einstein vacuum field equations with cosmological constant or a solution of the Einstein–Maxwell equations such that one principal null direction of the electromagnetic field is geodetic and shear-free.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528312
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  • 8
    Electronic Resource
    Electronic Resource
    The Teukolsky–Starobinsky identities in type D vacuum backgrounds with cosmological constant (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 2078-2083 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that in all the type D solutions to the Einstein vacuum field equations with cosmological constant, the one-variable functions appearing in the separable maximal spin-weight components of the neutrino, electromagnetic, and gravitational perturbations are related by certain differential operators and the corresponding proportionality constants are obtained. It is also shown that analogous relations hold in the case of perturbations by a Rarita–Schwinger field if the cosmological constant vanishes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527865
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  • 9
    Electronic Resource
    Electronic Resource
    Lanczos potential for some type D space–times (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 195-200 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A Lanczos potential of any non-null orbit type D solution of the Einstein–Maxwell equations with nonsingular aligned electromagnetic field is obtained. In the case of the Kerr–Newman solution the Lanczos potential is also explicitly given. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531300
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  • 10
    Electronic Resource
    Electronic Resource
    Gravitational perturbations of type-D vacuum space–times with cosmological constant (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3051-3058 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that in a type-D vacuum space–time with cosmological constant, the maximal spin weight components of the Weyl spinor perturbations, which obey separable decoupled equations, satisfy certain differential relations that are equivalent to the Teukolsky–Starobinsky identities fulfilled by the separated functions. It is also shown that the real and imaginary parts of the Starobinsky constants can be obtained from these relations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530504
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