Thermodynamical description of hot rapidly rotating neutron stars and neutron stars merger remnant

The prediction of the equation of state of hot dense nuclear matter is one of the most complicated and interesting problems in Nuclear Astrophysics. At the same time, its knowledge is the basic ingredient for some of the most interesting studies. In the present work we concentrate our study on the construction of the equation of state of hot dense nuclear matter, related mainly to the interior of the neutron star core. We employ a theoretical nuclear model, which includes momentum dependent interaction among the nucleons, along with the \textit{state-of-the-art} microscopic calculations. Thermal effects are introduced in a self-consistent way and a set of isothermal equations of state are predicted. The predicted equations of state are used in order to acquire and to extend the knowledge of thermal effect both on non-rotating and rapidly rotating with the Kepler frequency neutron stars. The simultaneously study of thermal and rotation effect provide useful information for some of the most important quantities, including the mass (gravitational and baryon) and radius, the Kepler frequency and kerr parameter, the moment of inertia etc. These quantities are directly related to studies of proto-neutron stars and mainly the hot and rapidly rotating remnant of a binary neutron stars merger. Data from the late observations of binary neutron stars mergers and the present study may offer useful tools for their investigation and help in providing possible constraints on the equation of state of nuclear matter.