Critical Mass Thresholds for Neutron Star Stability and Black Hole Formation in Gravitational Collapse

This research investigates the critical mass thresholds for black hole formation during the gravitational collapse of massive stars. Using numerical simulations and analytical techniques, we model the collapse of spherically symmetric, non-rotating neutron stars by solving the Tolman-Oppenheimer-Volkoff (TOV) equation. We first derive an analytical solution for the TOV equation under the assumption of constant density, estimating the maximum neutron star mass to be 2.85 solar masses. We then incorporate a customized density profile, as predicted in our previous work, into the TOV framework. This yields a critical mass of 2.096 solar masses at a radius of approximately 10 km, consistent with current theoretical and observational expectations. The maximum stable mass with this profile is calculated to be 2.36 solar masses, with the mass decreasing to zero beyond 15.5 km. By analyzing different initial masses (2.0, 4.0, and 8.0 solar masses) using a polytropic equation of state (EOS), we examine the mass-radius and pressure-radius relationships. Our results reveal a highly non-linear and abrupt change in mass and pressure distributions, indicating the formation of a dense outer shell. This structural feature could significantly influence neutron star stability and the conditions leading to black hole formation. These findings provide valuable insights into the maximum mass limits of neutron stars, aiding in the interpretation of astrophysical observations and the identification of potential black hole progenitors.