J B Griffiths and M Santano-Roco 2002 Class. Quantum Grav. 19 4273 doi:10.1088/0264-9381/19/16/304
J B Griffiths and M Santano-Roco
Show affiliationsThe 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.
04.30.Nk Wave propagation and interactions
04.20.Ex Initial value problem, existence and uniqueness of solutions
Issue 16 (21 August 2002)
Received 29 April 2002
Published 30 July 2002
J B Griffiths and M Santano-Roco 2002 Class. Quantum Grav. 19 4273
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