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- W2895608313 abstract "Einstein's equations are nonlinear, therefore, when gravitational waves meet, theymust interact. This interaction process has been studied in detail for some cases,particularly those involving plane waves. To understand the structure of thespace-time resulting from collisions of this type, many solutions have been generated.However, these have been obtained by first taking a candidate resultingspace-time, and then extending it back to give rise to the originating waves. Whilethese techniques are not too complex, it is not an easy task to obtain physicallyacceptable initial waves, and this is the greatest disadvantage of this indirectmethod.The main aim of this thesis is to consider a direct approach, to find a methodthat can overcome the difficulties indicated above, giving rise to solutions fromarbitrary colliding plane waves. A well posed initial value problem is formulatedfor the collinear case. This is achieved by making use of generalised Abel transforms. This method is successfully tested for some particularly well-known cases.However, when it is applied to more general cases, a number of problems arise.Along the direct and inverse transformation process, there are several successiveintegrations involved, and it is in these integrations that the main difficultiesappear, as the integrands themselves contain elliptic integrals.Nevertheless, a final way is found to obtain a final solution, which gives thesolution as a series expansion involving hypergeometric functions. Consequently,assuming we can obtain the spectral functions generated by the Abel transforms,the problem would be theoretically solved, although the calculations tend tobecome extremely complicated when arbitrary colliding waves are taken." @default.
- W2895608313 created "2018-10-12" @default.
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- W2895608313 date "2003-01-01" @default.
- W2895608313 modified "2023-09-27" @default.
- W2895608313 title "The initial value problem for colliding plane waves: the linear case" @default.
- W2895608313 hasPublicationYear "2003" @default.
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