Physical viability of fluid spheres satisfying the Karmarkar condition

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-behaves for 0.1574 ≤ c ≤ 0.46, 0.1235 ≤ c ≤ 0.35 and 0.05 ≤ c ≤ 0.13 respectively. The behavior of the thermodynamical and physical variables of these compact objects lead 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.

Radiating star with a time-dependent Karmarkar condition

“…It is also interesting to note that the Karmarkar condition together with the assumption of pressure isotropy picks out the interior Schwarzschild solution as the only bounded matter configuration. Recent attempts at modeling compact objects such as 4U 1538-52,PSR J1614-2230, Vela X-1 and Cen X-3 using the Karmarkar condition have been highly successful in producing stellar characteristics such as radius, mass, compactness and redshift which are consistent with observations [26][27][28][29][30][31][32]. In our present work we employ the Karmarkar condition to generate a nonstatic model of a radiating star.…”

Anisotropic fluid spheres of embedding class one using Karmarkar condition

“…Recently, Singh et al [40] have employed the HarrisonZeldovich-Novikov [41,42] criterion for investigating the stability of the anisotropic compact star models (Fig. 12).…”

A family of charged compact objects with anisotropic pressure

“…Work on rotating stars utilise an axis-symmetric metric to describe the stellar interior [11,12]. Recently there has been a surge in obtaining exact solutions of the Einstein field equations via embedding [13][14][15][16][17][18][19][20][21]. In 1947 Karmarkar obtained a restriction which is a necessary condition for embedding a spherically symmetric spacetime in four dimensions into a flat five-dimensional spacetime.…”