Gravitational collapse of massive stars and EOS

The importance of equations of state (EOS's) will be elucidated by their applications to gravitational collapse of massive stars, the common event that occurs at the end of their lives. Future detections of neutrinos (and gravitational waves) from nearby events will provide us with the opportunity to probe the properties of hadronic matter that may not be accessible by terrestrial experiments, particularly in the event of black hole formations. In this chapter, thermodynamical states in the collapsing stellar cores and EOS's that have been employed frequently to describe them in the literature will be reviewed for sub- and supra-nuclear densities separately. The roles these EOS's play in the dynamics of gravitational collapse and some observational consequences that their uncertainties may have will be presented from exemplary numerical simulations.