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We present model for anisotropic compact star under the general theory ofrelativity of Einstein. In the study a 4-dimensional spacetime has beenconsidered which is embedded into the 5-dimensional flat metric so that thespherically symmetric metric has class 1 when the condition$e^{\lambda}=\left(\,1+C\,e^{\nu} \,{\nu'}^2\,\right)$ is satisfied ($\lambda$and $\nu$ being the metric potentials along with a constant $C$). A set ofsolutions for the field equations are found depending on the index $n$ involvedin the physical parameters. The interior solutions have been matched smoothlyat the boundary of the spherical distribution to the exterior Schwarzschildsolution which necessarily provides values of the unknown constants. We havechosen the values of $n$ as $n=2$ and $n$=10 to 20000 for which interesting andphysically viable results can be found out. The numerical values of theparameters and arbitrary constants for different compact stars are assumed inthe graphical plots and tables as follows: (i) LMC X-4 : $a=0.0075$,$b=0.000821$ for $n=2$ and $a=0.0075$, $nb=0.00164$ for $n\ge 10$, (ii) SMCX-1: $a=0.00681$, $b=0.00078$ for $n=2$, and $a=0.00681$, $nb=0.00159$ for $n\ge 10$. The investigations on the physical features of the model includeseveral astrophysical issues, like (i) regularity behavior of stars at thecentre, (ii) well behaved condition for velocity of sound, (iii) energyconditions, (iv) stabilty of the system via the following three techniques -adiabatic index, Herrera cracking concept and TOV equation, (v) total mass,effective mass and compactification factor and (vi) surface redshift. Specificnumerical values of the compact star candidates LMC X-4 and SMC X-1 arecalculated for central and surface densities as well as central pressure tocompare the model value with actual observational data.

A generalized family of anisotropic compact object in general relativity