Title: A generalized family of anisotropic compact object in general relativity,
Abstract: We present model for anisotropic compact star under the general theory of
relativity of Einstein. In the study a 4-dimensional spacetime has been
considered which is embedded into the 5-dimensional flat metric so that the
spherically 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 of
solutions for the field equations are found depending on the index $n$ involved
in the physical parameters. The interior solutions have been matched smoothly
at the boundary of the spherical distribution to the exterior Schwarzschild
solution which necessarily provides values of the unknown constants. We have
chosen the values of $n$ as $n=2$ and $n$=10 to 20000 for which interesting and
physically viable results can be found out. The numerical values of the
parameters and arbitrary constants for different compact stars are assumed in
the 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) SMC
X-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 include
several astrophysical issues, like (i) regularity behavior of stars at the
centre, (ii) well behaved condition for velocity of sound, (iii) energy
conditions, (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. Specific
numerical values of the compact star candidates LMC X-4 and SMC X-1 are
calculated for central and surface densities as well as central pressure to
compare the model value with actual observational data.