A comparative study on maximum mass and radius of compact star from Heintzmann geometry and TOV approach

In this article a class of anisotropic compact star is analysed in Heintzmann geometry. We have introduced the pressure anisotropy parameter ($\alpha$) and solved Einstein field equations to obtain stellar model. We have considered $g_{tt}$ component as proposed by Heintzmann and by solving Einstein field equation, the $g_{rr}$ component is evaluated in presence of pressure anisotropy. It is noted that for isotropic star ($\alpha=0$), the maximum mass lies within the range $1.87-3.04~ M_{\odot}$ for radii ranges between $8-13$ Km. For anisotropic compact stars maximum mass increases with $\alpha$ and lies within the range $1.99-3.23~ M_{\odot}$ for anisotropy parameter $\alpha=0.5$. The physical viability of the model is examined by applying our model to study the properties of few known compact objects. It is noted that all the stability conditions are fulfilled in the proposed model. It is interesting to note that maximum mass calculated from our model and from solving TOV equation are approximately same and also the predicted radius of few newly observed pulsars and companion star of GW events GW 190814 and GW 170817 from our model comply with the estimated value of radius from observation.