Applications of NP Formalism and GHP Formalism in General Relativity

Doctoral Thesis / Dissertation from the year 2017 in the subject Mathematics - Applied Mathematics, grade: NA, Sardar Patel University (Department of Mathematics), language: English, abstract: Einstein proposed general relativity theory in 1915, this theory most successfully describes gravity. A typical approach to analyze gravitational field of an object is to solve Einstein's field equations, in this approach the assumptions are guided by observations and they help in understanding physical aspects. From mathematical stand point of view we may look for geometric tools. In recent times, tetrad formalisms like Newman-Penrose formalism and Geroch-Held-Penrose formalism are popular to analyze gravitational field. Tetrad formalisms are based on choosing a suitable set of basis vectors for the spacetime under consideration. For using a tetrad formalism the relevant quantities are projected on to the chosen basis and the equations satisfied by them are considered. In this thesis, we have developed some applications of the NP formalism and GHP formalism to electromagnetic gravitational analogies, (i) electric and magnetic parts of the Weyl tensor and (ii) Lanczos potential. The complication involved in the computations compelled us to pay some attention to work in computer aided algebraic computations.