Stellar Solutions in Rastall Modified Gravity by Embedding Technique

Abstract

In this thesis, we discuss the compact stars models with the anisotropic mat- ter distribution in the context of Rastall theory of gravity. We solve the Rastall field equations by taking into account spherically symmetric line element. We construct the stellar models with the help of embedding technique. In order to achieve the purpose, first we choose the Karmarker condition with grr compo- nent of metric space as eλ(r) = 1 + cr2(1+ar2) n (1+br2)2 . We find the solutions for different values of Rastall parameter. We analyze the properties of stellar model by taking into account observational data of a compact star, named Vela X-1. We take into account different positive values of n and observe the scenario regarding the physical acceptability of the solution by presenting graphical analysis of ther- modynamical quantities, i.e., ρ, pr and pt. Next, we choose Karmarker condition with another radial component, i.e., eλ = (A − Br2) 2 and analyze the viability of model considering observational data of compact stars, namely CenX − 3, PSRJ1614 − 2230 and, LMCX − 4. In order to check the physical viability of the solution, we discuss energy condition, TOV equilibrium condition, causal- ity condition and stability condition through graphical analysis. We have also presented variation of gradients, EoS, red-shift function and mass function. We find our solutions physical well-behaved for different values of n in the case of first model, while the graphical description of second stellar model guarantees its physical acceptability.