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 e
λ(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., e
λ = (A − Br2
)
2
and analyze the viability
of model considering observational data of compact stars, namely CenX − 3,
P SRJ1614 − 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
