Relativistic massive compact stars supported by decoupled matter: Implications for mass-radius bounds

The merger of binary neutron stars (BNSs) is a remarkable astrophysical event where all four fundamental forces interplay dynamically across multiple stages, producing a rich spectrum of multi-messenger signals. These observations present a significant multiphysics modeling challenge but also offer a unique opportunity to probe the nature of gravity and the strong nuclear interaction under extreme conditions. The landmark detection of GW170817 provided essential constraints on the properties of non-rotating neutron stars (NSs), including their maximum mass (M_{max}) and radius distribution, thereby informing the equation of state (EOS) of cold, dense nuclear matter. While the inspiral phase of such events has been extensively studied, the post-merger signal holds even greater potential to reveal the behavior of matter at supranuclear densities, particularly in scenarios involving a transition to deconfined quark matter. Motivated by the recent gravitational wave event GW190814 (2.5-2.67 M_{\odot}), we revisit the modeling of high-mass compact stars to investigate their internal structure via a generalized polytropic EOS. This framework incorporates a modified energy density profile and is coupled with the TOV equations. We explore mass-radius (M-R) relationships within both GR and the minimal geometric deformation (MGD) approach. Specifically, we constrain the radii of four massive compact objects PSR J1614-2230 (1.97^{+0.04}_{-0.04}\,M_{\odot}), PSR J0952-0607 (2.35^{+0.17}_{-0.17}\,M_\odot), GW190814 (2.5-2.67\,M_\odot), and GW200210 (2.83^{+0.47}_{-0.42}\,M_\odot) and demonstrate that our theoretical M-R curves are consistent with observational data. These findings provide meaningful constraints on the EOS and underscore the potential of alternative gravity models to accommodate ultra-massive compact stars within a physically consistent framework.