Abstract
We obtain a new static model of the TOV equation for an anisotropic fluid distribution by imposing the Karmarkar condition. In order to close the system of equations we postulate an interesting form for the g_{rr} gravitational potential, which allows us to solve for g_{tt} metric component via the Karmarkar condition. We demonstrate that the new interior solution has well-behaved physical attributes and can be utilized to model relativistic static fluid spheres. By using observational data sets for the radii and masses for compact stars such as 4U 1538-52, LMC X-4, and PSR J1614-2230 we show that our solution describes these objects to a very good degree of accuracy. The physical plausibility of the solution depends on a parameter c for a particular star. For 4U 1538-52, LMC X-4, and PSR J1614-2230 the solutions are well behaved for 0.1574 le c le 0.46, 0.1235 le c le 0.35 and 0.05 le c le 0.13, respectively. The behavior of the thermodynamical and physical variables of these compact objects leads us to conclude that the parameter c plays an important role in determining the equation of state of the stellar material and observed that smaller values of c lead to stiffer equation of states.
Highlights
The Einstein field equations describing localized bodies is a system of highly nonlinear partial differential equations which are difficult in general
C (2017) 77:100 stein field equations which connects the curvature of spacetime to the matter content which allows one to either specify the geometry or the matter distribution to determine the behavior of the other
The relaxation of the pressure isotropy condition has led to an explosion of exact solutions of the Einstein field equations describing compact objects
Summary
The Einstein field equations describing localized bodies is a system of highly nonlinear partial differential equations which are difficult in general. In seeking solutions to these equations various novel ideas ranging from an ad-hoc specification of the gravitational potentials, imposing an equation of state, prescribing the behavior of the density, pressure or anisotropy profiles ab initio and specifying the spacetime symmetry have been utilized It is the very nature of the Ein-. Based on fundamental particle interactions the standard linear equation of state has been extended to include the bag constant This equation of state has been used extensively to model compact objects with anisotropic pressure profiles as well as a non-vanishing electromagnetic field in the stellar interior. The necessary and sufficient condition for a spherically symmetric spacetime to be of embedding class I was first derived by Karmarkar [41] It is a mathematical simplification which reduces the problem of obtaining exact solutions to a single-generating function. We subject our solutions to rigorous physical tests which ensure that they do describe physically observable objects in the universe
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