02-26.pdf (187.19 kB)
The characteristic initial value problem for colliding plane waves: the linear case
preprint
posted on 2005-08-25, 14:13 authored by Jerry Griffiths, Miguel Santano-RocoThe 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.
History
School
- Science
Department
- Mathematical Sciences
Pages
191686 bytesPublication date
2002Notes
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.Language
- en