Study On Stellar Structures And Wormhole Modeling In Modified Theories Of Gravity

This thesis is devoted to exploring the mathematical background of stellar structures and wormhole modeling in different modified theories of gravity.To meet this aim,we choose f(G),f(R,G),f(G,T),f(R,T)theories for stellar study.Modified telleparallel theories,in particular,F(?,?_G)theory of gravity is chosen for wormhole modeling.The spherically symmetric spacetime with the anisotropic fluid distribution is considered in this thesis work.The embedded class one spacetime via Karmarkar condition is used to explore the compact star solutions in f(G),f(R,G),f(G,T),f(R,T)theories of gravity.Further,we use the observational data of the specific model of compact stars namely LMCX-4,Cen X-3,EXO1785-248,4U 1538-52,and PS R J1614-2230.We develop the field equations for f(G),f(R,G),f(G,T),f(R,T)theories of gravity by using embedded class one spacetime.We further consider the Schwarzschild geometry for matching conditions at the boundary.It is important to mention here that we calculate all the involved parameter values by imposing the matching condition.We have provided a detailed graphical analysis to discuss the physical acceptability of parameters,i.e.,energy density,pressure,anisotropy,and gradients.We have also examined the stability of stellar structures by exploring the energy conditions,equation of state,generalized Tolman-Oppenheimer-Volkoff equation,causality condition,and adiabatic index.We predict some numerical values in tabular form for central gravitational metric functions,central density,and central pressures components for the present analysis.We have also calculated the ratio p_rc/?_cto check the validity of Zeldovich's condition.Conclusively,it is found that our obtained solutions are physically viable with well-behaved nature in f(G),f(R,G),f(G,T),f(R,T)theories of gravity for the compact star models under discussion.We discuss the existence of wormhole solutions in F(?,?_G)theory of gravity with the assumption that the matter density profile satisfies the Gaussian and Lorentzian distributions.Further,for the solutions of field equations in F(?,?_G)theory of gravity,we have used the different models of F(?,?_G)theory of gravity.For these specific models,we have calculated the feasible solutions for the existence of wormholes by using the conformal symmetry approach.A detailed analysis of energy conditions is provided for F(?,?_G)theory of gravity.The violation of the null energy condition confirms the presence of exotic matter in both theories.The stability of obtained wormholes solutions by using the modified Tolman Oppenheimer Volkoff equation in terms of different forces is checked for F(?,?_G)theory of gravity.In the presence of Lorentzian and Gaussian distributions with conformal symmetry,it has been shown that stable wormhole solutions would exist for particular values of parameters.