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Title: The characteristic initial value problem for colliding plane waves: the linear case
Authors: Griffiths, J.B.
Santano-Roco, M.
Issue Date: 2002
Abstract: 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.
Description: This pre-print has been submitted, and accepted, to the journal, Classical and Quantum Gravity [© Institute of Physics]. The definitive version: GRIFFITHS, J.B. and SANTANO-ROCO, M., 2002. The characteristic initial value problem for colliding plane waves: the linear case. Classical and Quantum Gravity, 19(16), pp.4273-4286, is available at: http://www.iop.org/EJ/journal/CQG.
URI: https://dspace.lboro.ac.uk/2134/459
Appears in Collections:Pre-prints (Maths)

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