Abstract
The present study is devoted to explore the existence of a new family of compact star solutions by adopting the Karmarkar as well as Pandey–Sharma condition in the background of f ( R , T ) modified gravitational framework. For this purpose, we consider static spherically symmetric spacetime with anisotropic fluid distribution in absence of electric charge. In respect of Karmarkar condition, we assume a specific model of g r r metric potential representing a new family of solutions which is also compatible with the Pandey–Sharma condition. This assumed model permits us to calculate the g t t component of metric tensor by making the use of Karmarkar condition. Further, we investigate the interior solutions for V e l a X − 1 model of compact star by utilizing this new family of solutions for different values of parameter λ . We have tuned the solution for V e l a X − 1 so that the solutions matches the observed mass and radius. For the same star we have extensively discussed the behavior of the solutions. It is found that these solutions fulfill all the necessary conditions under the observational radii and mass attribute data for small values of parameter λ and hence physically well-behaved and promising. Through graphical analysis, it is observed that our obtained analytical solutions are physically acceptable with a best degree of accuracy for n ∈ [ 1.8 , 7 ) − { 2 , 4 , 6 } , where parameter n is involved in the discussed model. It is also noticed the causality condition is violated for all n ≥ 7 and the tangential sound velocity v t is observed as complex valued for all 0 < n < 1.8 . Likewise, we explore these properties by considering large parameter λ values. It is seen that the presented model violates all the physical conditions for n ∈ { 2 , 4 , 6 } , while some of these for large values of λ . Consequently, it can be concluded that the parameters n and λ have a strong impact on the obtained solutions.
Highlights
The study of relativistic compact stars in the background of general relativity (GR) and extended theories of gravity is considered as one of the most promising subjects among the researchers during last few decades
The present study investigates the existence of spherical symmetric solutions for Vela X − 1 model of compact stars in the framework of f (R, T ) theory of gravity
The solid graphs illustrate the current development of the energy density function for 1.8 ≤ n < 7 and the dashed graphs refer to its behavior for n = 7
Summary
The study of relativistic compact stars in the background of general relativity (GR) and extended theories of gravity is considered as one of the most promising subjects among the researchers during last few decades. It is argued that GR theory faced stringent constraints for describing the galactic scale, the strong lensing regime and CMBR tests In this respect, its recently proposed extended version namely f (R ) theory is considered as quite successful and interesting because of its correspondence to scalar-tensor gravity, i.e., the GR with an extra scalar-field candidate, whose scalar-potential is in double correspondence to the generic function f [24]. The present study investigates the existence of spherical symmetric solutions for Vela X − 1 model of compact stars in the framework of f (R, T ) theory of gravity. For this purpose, we shall adopt the Karmarkar as well as Pandey Sharma condition for simplification purposes.
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