Maximum mass of an anisotropic compact object admitting the modified Chaplygin equation of state in Buchdahl-I metric

In this article, a new class of exact solutions for anisotropic compact objects is presented. Admitting the modified Chaplygin equation of state $p=H\rho-\frac{K}{\rho^{n}}$, where $H$, $K$ and $n$ are constants with $0<n\leq1$, and employing the Buchdahl-I metric within the framework of the general relativity stellar model is obtained. Recent observations on pulsars and GW events reveal that the observed maximum mass of compact stars detected so far is approximately $2.59^{+0.08}_{-0.09}~M_{\odot}$. Since massive stars cannot be supported by a soft equation of state, a constraint of the equation of state must hold. The choice of a suitable equation of state for the interior matter of compact objects may predict useful information compatible with recent observations. TOV equations have been solved using the modified Chaplygin equation of state to find the maximum mass in this model. In particular, the theory can achieve $3.72~M_{\odot}$, when $H=1.0$, $K=10^{-7}$ and $n=1$. The model is suitable for describing the mass of pulsars PSR J2215+5135 and PSR J0952-0607 and the mass $2.59^{+0.08}_{-0.09}~M_{\odot}$ of the companion star in the GW 190814 event. The $3.72~M_{\odot}$ is hardly achievable theoretically in general relativity considering fast rotation effects too. To check the physical viability of this model, we have opted for the stability analysis and energy conditions. We have found that our model satisfies all the necessary criteria to be a physically realistic model.