TEORI RELATIVITAS UMUM DALAM PENDEKATAN GEOMETRI DIFERENSIAL DAN ALIHRAGAM BÄCKLUND SEBAGAI METODE PENCARIAN JAWABAN ANALITIK BAGI MEDAN STASIONER VAKUM SETANGKUP GANDAR ROTASI DIFFERENTIAL GEOMETRY IN GENERAL RELATIVITY AND BÄCKLUND TRANSFORMATIONS AS A METHODS TO FIND AN EXACT SOLUTIONS OF STATIONARY AXIALLY SYMETRICS VACUUM SPACE-TIME

SUBAGIYO, M. Farchani Rosyid

2015 | Skripsi | FMIPA

General relativity and Bäcklund transformation have been studied here. In this work, Bäcklund transformation is used to find the exact solutions of Enstein’s fields equations of vacuum stationary, axially symetric space-times. The exact solutions of Einstein’s fields equation is too important in the theoritical physics. Using the exact solutions of Einstein’s field equation, the physicist not only can study the structure of space-times but also can understood space-times’s structure itself. In fact, there are some problems and difficulties in the way of looking for the exact solutions of Einstein’s fields equation. The first problem rising from the fact that the Einstein’s equation is not a linear equations. Because of the Einstein’s equation is not a linieaR, it implies that there is no unique solution that satisfied all of the posibilities of spacetimes structure. The other dificulties is come from the fact that there is no one general methods that can be applied to looking for the solutions of the non-liniear partial differential eqations. To find the exact solutions of the Einstein’s fields equation, the scientists have been developed some methods of finding the solutions of non-liniear partial differential equations system. Among of the methods, that is Bäcklund transformation. Bäcklund transformation relates the solutions of the non-liniear partial differential equation to the other one. In simple meaning, we can obtain the other solutions from the other one known solution. The other one known solution then called by ’seed solution’. In this work, have been studied about the using of Bäcklund transformation in the looking for the exact solutions of Einstein’s fields equation of the vacuum stationary, axially symetric space-times. Using the Bäcklund transformation methods and Minkowski solutions as a seed solution, we can obtain the other one solution of Einstein fields equation. There is Kerr-NUT solution. This writting has been made by literature research in some of books and journals about general relativity, differential geometry, Bäcklund transformation and the other related articles.

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