The characteristic initial value problem for colliding plane waves: The linear case

Details The characteristic initial value problem for colliding plane waves: The linear case The characteristic initial value problem for colliding plane waves: The linear case

2002-06-25

arxiv.org/abs/gr-qc/0206075v1

Class.Quant.Grav. 19 (2002) 4273-4286

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages. To appear in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/19/16/304

The physical situation of the collision and subsequent interaction of plane gravitational waves in a Minkowski background gives rise to a well-posed characteristic initial value problem in which initial data are specified on the two null characteristics that define the wavefronts. In this paper, we analyse how the Abel transform method can be used in practice to solve this problem for the linear case in which the polarization of the two gravitational waves is constant and aligned. We show how the method works for some known solutions, where problems arise in other cases, and how the problem can always be solved in terms of an infinite series if the spectral functions for the initial data can be evaluated explicitly.

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