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Title Teleparallel Killing Vector Fields of Static Spherically Symmetric Space-Times in f(T) gravity.

Author(s) Nazish Mahroof

Abstract Symmetries principle play a crucial role in solving various problems,as they underpin conservation laws and fundamental interactions. The connection between conservation principle and symmetry in physics is both fundamentally important and highly useful. Curved space-time symmetries are produced by Killing vectors, also known as isometries. These symmetries aid in the classification and solution solving in connection with Einstein field equations (EFEs). As a result, symmetries are important for explaining space-time geometry. A fascinating theory that has gained traction in recent decades is teleparallel gravity (TG) in which torsion takes the place of curvature. It accomplishes by this replacing the Levi-Civita connection, which is built on curvature, with a teleparallel connection, which is based on torsion. This thesis provides a comprehensive analysis of Teleparallel Killing vector fields (TKVFs) of static spherically symmetric space-times within the framework of f (T) gravity, an extended theory of gravity based on torsion rather than curvature. Static spherically symmetric solutions to Einstein field equations in f (T) gravity have already been existed in the literature.The classification of those solutions via TKVFs have been done. In this study, 20 distinct solutions have been explored. Ten coupled partial differential equations were obtained for each solution. To determine the TKVFs these equations were solved using the direct integration technique. Teleparallel Killing vector fields were found in all those 20 cases. Every scenario is thoroughly examined to investigate the ways in which the changed gravity framework affects the presence and characteristics of teleparallel Killing vector fields. The study concludes with a thorough analysis of the findings that emphasizes the main distinctions from general relativity.

Type Thesis/Dissertation MS

Faculty Engineering and Computer Science

Department Mathematics

Language English

Publication Date 2025-06-04

Subject Mathematics

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