Dynamics of Stellar Structures in Curvature Based Gravitational Theories

Abstract

The main objective of this thesis is to explore different astrophysical structures in the background of general relativity as well as in the framework of modified theories. Firstly, we discuss the minimal geometric deformation (MGD) decoupling approach to develop new exact anisotropic solutions for compact stellar systems in the absence as well as in the presence of the electromagnetic field. We consider two well-known solutions, namely Tolman V and charged Durgapal V, and extend them to anisotropic domains by transforming their radial metric functions. The physical analysis of the new interior anisotropic solutions is performed by examining the graphical behavior of energy conditions, equilibrium condition, causality condition, adiabatic index and gravitational redshift for different compact star candidates. Secondly, we develop two analytical models of ultra-compact stellar configurations with non-uniform anisotropic features in the framework of 𝑓(𝑅, 𝑇) theory. In order to introduce anisotropy in the system, we again consider gravitational decoupling by means of MGD and obtain two families of interior solutions for both charged and uncharged scenarios. Dark energy EoS is considered in the interior of the configuration. In the exterior region, we consider both standard vacuum and conformally deformed black hole solutions. The junction conditions at the stellar boundary for both charged and uncharged stellar sources are presented in detail. Some fundamental properties of a stable configuration including regularity at the center, positive energy density with monotonically decreasing behavior from the center outwards, and non-uniform pressure with the monotonic profile are checked for the new anisotropic solutions. Finally, the complexity analysis of non-static spherically and cylindrically symmetric self-gravitating sources surrounding in the locally anisotropic environment and suffering dissipation in the form of heat flux is presented in the light of 𝑓(𝑅, 𝑇) gravity. Our study is based on the definition of complexity for dynamical self-gravitating sources, proposed by Herrera et al. [68]. The scalar functions through the orthogonal splitting of the Riemann tensor are defined in 𝑓(𝑅, 𝑇) gravity, and structure scalars are worked out for both geometries. Our main objective is to analyze the behavior of