On gauge freedom for separability of waves in spherically symmetric spacetime and perturbations in Schwarzchild geometry

Snegupta, Sohan (2022) On gauge freedom for separability of waves in spherically symmetric spacetime and perturbations in Schwarzchild geometry. Masters thesis, Indian Institute of science Education and research Kolkata.

Text (MS dissertation of Sohan Sengupta (17MS215)) 17MS215_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (281kB)

Abstract

For most of us Wave equations in curved spacetime are much more complicated than flat Minskowski spacetime. Separability of wave solutions are shown to exists in some wave operators. Here we have shown that separability can be achieved in curved spacetime as well. To achieve these class of separable solutions we investigated the conditions or constraints in the elements of metric matrix specifically in spherically symmetric and axially symmetric spacetime. We further noticed that these constraints must hold even with shift in coordinate systems, specially named as gauge freedom. We investigated individually for simple scalar, vector and tensor waves in both spher- ically and axially symmetric spacetime. A gauge freedom is formal the freedom of choice of coordinates one can have after a gauge transformation in the chosen coordi- nates. Solutions of wave equation in schwarzchild geometry has been already achieved for scalar waves but for a general spherically symmetric system we investigated the solution. We also investigated the solution for vector and tensor waves in spherical and axial symmetric spacetime. This work is a well focused problem in perturbation theory of General Relativity. Therefore, we went a step ahead to achieve the equations of perturbation in spherically symmetric spacetime.

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