Initial value problem for colliding gravitational plane waves. III

Journal Article · Sun Apr 01 04:00:00 EDT 1990 · Journal of Mathematical Physics (New York); (USA)

DOI:https://doi.org/10.1063/1.528822· OSTI ID:6847076

Hauser, I ^[1]; Ernst, F J ^[2]

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1. Department of Mathematics Department of Computer Science, Clarkson University, Potsdam, New York 13675 (USA)
2. Department of Mathematics Department of Computer Science, Clarkson University, Potsdam, NY (USA) Department of Physics, Clarkson University, Potsdam, NY 13676 (USA)

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. {bold 30}, 872 (1989) and {bold 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, Garcia, and Hauser (J. Math. Phys. {bold 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.

• OSTI ID: 6847076
• Journal Information: Journal of Mathematical Physics (New York); (USA), Journal Name: Journal of Mathematical Physics (New York); (USA) Vol. 31:4; ISSN JMAPA; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY-VALUE PROBLEMS
COLLISIONS
EQUATIONS
FREDHOLM EQUATION
GRAVITATIONAL WAVES
HILBERT TRANSFORMATION
INTEGRAL EQUATIONS
INTEGRAL TRANSFORMATIONS
MATRICES
POLARIZATION
TRANSFORMATIONS