Theoretical Equation of State for Neutron Stars, its Maximal Mass in the Framework of General Relativity before Collapsing into a Black Hole

Despite significant advancements in multi-messenger astronomy and gravitational wave detection, the accurate determination of EOS for NS remains a critical challenge in astrophysics. Current theoretical models often fail to comprehensively reconcile the fundamental properties of NS such as the maximum mass, with observational evidence. The gap limits the full understanding of the maximum stable mass and density of NS, as well as it behavior under extreme relativistic conditions. Computational tools like Einstein’s toolkit and recent multi-massagers observations by LIGO and Virgo have provided useful data, there is a lack of unified, precise EOS models’ that incorporate both theoretical and observational constraints. Addressing this problem is essential for advancing our understanding of NS physics and for guiding future observations. This research therefore, aims to address these gaps by constructing a robust theoretical EOS models for NS using piecewise polytrope approach based on general relativity, supported by computational simulations and validate same against existing observational data. An EOS constructed from theoretical models and numerical simulations has revealed that a NS can attain a maximum mass of before collapsing into a BH at a radius of up to 12 km, based on the mass-radius relationship derived from the model.