Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Initial value problem for colliding gravitational plane waves. I (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 872-887 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new form of the general solution of the initial value problem for colliding gravitational plane waves with collinear polarization is obtained. The solution of the linear hyperbolic field equation for ψ(u,v) is expressed as a linear superposition ∫da g(σ)ω(u,v,σ) of a one-parameter family of basic solutions of the form ω(u,v,σ)=ω1(u,σ)ω2(v,σ), where u and v are arbitrary null coordinates and σ is the parameter. The coefficients g(σ) in this superposition are expressed in terms of the initial data by using a generalization of an integral transform obtained by Abel in his solution of a tautochrone problem of classical particle mechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528355
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Colliding gravitational plane waves with noncollinear polarization. III (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 681-689 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Hauser–Ernst homogeneous Hilbert problem (HHP) approach, formerly used in connection with the derivation of stationary axisymmetric fields, is here adapted to the derivation of colliding gravitational plane wave solutions of the vacuum Einstein equations. Proceeding from Kasner metrics, and using a double-Harrison transformation, the HHP approach yields a three-parameter generalization of a two-parameter family of colliding wave solutions found recently by Ferrari, Ibañez, and Bruni. In the present paper we provide the details concerning the derivation of this new family of solutions, and we set the stage for future applications of the HHP approach in connection with gravitational waves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528007
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Colliding gravitational plane waves with noncollinear polarization. I (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2155-2161 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An Ehlers transformation on the Ernst potential for the Nutku–Halil solution [Phys. Rev. Lett. 39, 1379 (1977)] provides a new solution of the Einstein field equations describing colliding gravitational plane waves with noncollinear polarization, the first of an infinite sequence of solutions that can be generated using techniques described in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527427
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Colliding gravitational plane waves with noncollinear polarization. II (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2951-2960 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple criterion for colliding gravitational plane waves is developed. This colliding wave condition is preserved by a new realization of the Geroch group augmented by a Kramer–Neugebauer involution. A three-parameter generalization of a two-parameter family of solutions with noncollinear polarization discovered recently by Ferrari, Ibañez, and Bruni is presented, and two additional solutions are derived that demonstrate that much larger families are likely to be constructed in the near future.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527698
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Nonimpulsive colliding gravitational waves with noncollinear polarizations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2478-2482 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new method of constructing solutions of the Einstein equations describing nonimpulsive colliding gravitational waves with noncollinear polarizations is introduced. Application of the procedure is illustrated by constructing a large family of such solutions of the vacuum Einstein equations. The new solutions are shown to possess Killing–Cauchy horizons when n+2δ1 is set equal to ±3 or ±1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529177
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    A family of electrovac colliding wave solutions of Einstein's equations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 678-682 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Beginning with any colliding wave solution of the vacuum Einstein equations, a corresponding electrified colliding wave solution can be generated through the use of a transformation due to Harrison [J. Math. Phys. 9, 1744 (1968)]. The method, long employed in the context of stationary axisymmetric fields, is equally applicable to colliding wave solutions. Here it is applied to a large family of vacuum metrics derived by applying a generalized Ehlers transformation to solutions published recently by Ernst, García, and Hauser (EGH) [J. Math. Phys. 28, 2155, 2951 (1987); 29, 681 (1988)]. Those EGH solutions were themselves a generalization of solutions first derived by Ferrari, Ibañez, and Bruni [Phys. Rev. D 36, 1053 (1987)]. Among the electrovac solutions that are obtained is a charged version of the Nutku–Halil [Phys. Rev. Lett. 39, 1379 (1977)] metric that possesses an arbitrary complex charge parameter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528607
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Initial value problem for colliding gravitational plane waves. III (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 871-881 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The development of a homogeneous Hilbert problem (HHP) approach to the initial value problem (IVP) for colliding gravitational plane waves with noncollinear polarization that began in two earlier papers [I. Hauser and F. J. Ernst, J. Math. Phys. 30, 872 (1989) and 30, 2322 (1989)] is continued. After formulating the HHP, the description of how one can apply it to generate a new family of solutions of the colliding wave problem that generalizes a three-parameter family constructed by Ernst, García, and Hauser [J. Math. Phys. 29, 681 (1988)] using a double-Harrison transformation is given. Then the proof that the solution of the new HHP indeed solves the IVP that is posed is presented. A matrix Fredholm equation of the second kind that is equivalent to the HHP is also deduced. This will be used in a sequel to complete the proof of existence of solutions of the HHP and the proof that certain assumed differentiability hypotheses are in fact valid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528822
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Colliding wave solutions of the Einstein–Maxwell field equations (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 1030-1034 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A large family of solutions of the vacuum Einstein equations [J. Math. Phys. 32, 723 (1991)] is generalized to the electrovac case. The new solutions are shown to possess Killing–Cauchy horizons when one of the parameters n is set equal to 3, 1, −1 or −3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529379
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Initial value problem for colliding gravitational plane waves. IV (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 198-209 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a preceding paper [I. Hauser and F. J. Ernst, J. Math. Phys. 31, 871 (1990)], the initial value problem for colliding gravitational plane waves was reformulated as a homogeneous Hilbert problem (HHP) in a complex plane. It is now proven that a unique solution of this HHP always exists and that any assumed differentiability or holomorphy properties of the plane-wave metrics imply corresponding properties for the scattered wave metric. This completes the demonstration, initiated in the preceding paper, that the solution of the HHP furnishes the solution of the initial value problem. A Fredholm equation that is equivalent to the HHP and that was introduced in the preceding paper is used to effect the proofs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529117
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Initial value problem for colliding gravitational plane waves. II (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2322-2336 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: As a preliminary step in the development of a Hilbert problem (HP) approach to the initial value problem (IVP) for colliding gravitational plane waves with noncollinear polarizations, the IVP for colliding gravitational plane waves with collinear polarizations is reformulated in two different ways as an HP in a complex plane. The solutions of both forms of the HP are found and each of these agrees with the solution obtained by another method in the previous paper of this series [I. Hauser and F. J. Ernst, J. Math. Phys. 30, 872 (1989)]. The conditions imposed on the initial data of the IVP by the vacuum field equations are discussed in detail. Anticipating the next paper of this series, the generalization of one form of the HP to noncollinear polarizations is briefly described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528562
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...