TEORI RELATIVITAS UMUM DALAM PENDEKATAN GEOMETRI DIFERENSIAL DAN ALIHRAGAM BACKLUND SEBAGAI METODE PENCARIAN JAWABAN ANALITIK BAGI MEDAN STASIONER VAKUM SETANGKUP GANDAR ROTASI

SUBAGIYO, Dr.rer.nat Muhammad Farchani Rosyid

2015 | Skripsi | S1 FISIKA

Telah dilakukan studi Literatur mengenai pendekatan geometri differensial dalam teori relativitas umum dan penggunaan alih-ragam Backlund sebagai salah satu metode untuk mendapatkan jawaban analitik bagi persamaan medan Einstein pada kasus medan vakum stasioner setangkup gandar rotasi. Pencarian jawaban analitik bagi persamaan medan Einstein merupakan hal yang penting dalam fisika teori. Hal ini disebabkan bentuk penyelesaian persamaan medan Einstein dapat digunakan untuk mempelajari dan memahami struktur ruang-waktu yang terkait dengan keberadaan medan gravitasi. Meskipun demikian, usaha untuk mendapatkan jawaban tersebut tidaklah mudah. Persamaan medan Einstein yang merupakan persamaan tak-linier mengakibatkan ketiadaan bentuk jawaban umum yang tunggal bagi persamaan tersebut. Guna mendapatkan penyelesaian persamaan medan Einstein, telah dikembangkan berbagai metode untuk menyelesaikan persamaan differensial tak-linier. Salah satu metode yang telah dikembangkan untuk menyelesaikan permasalahan persamaan differensial tak-linier adalah metode alih-ragam Backlund. Alih-ragam Backlund mengaitkan satu bentuk jawaban bagi suatu persamaan differensial tak-linier menuju ke bentuk jawaban lain. Dalam studi ini, telah dilakukan telaah mengenai penggunaan alih-ragam Backlund sebagai metode pencarian jawaban bagi persamaan medan Einstein dalam kasus medan stasioner vakum setangkup gandar rotasi. Dengan menggunakan metode alih-ragam Backlund dan benih jawaban berupa penyelesaian Minkowski, dapat diperoleh penyelesaian baru berupa potensial Ernst yang terkait dengan penyelesaian Kerr-NUT. Penelitian yang dilakukan adalah dengan melakukan studi literatur.

General relativity and Backlund transformation have been studied here. In this work, Backlund 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 space-times 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 Backlund transformation. Backlund 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 Backlund transformation in the looking for the exact solutions of Einstein's fields equation of the vacuum stationary, axially symetric space-times. Using the Backlund 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, Backlund transformation and the other related articles.

Kata Kunci : relativitas umum, penyelesaian analitik, persamaan medan Einstein, medan vakum stasioner setangkup gandar rotasi, alih-ragam Backlund, metrik Kerr-NUT.