Induced surface and curvature tensions equation of state of hadrons with relativistic excluded volumes and its relation to morphological thermodynamics

An analytical formula that accurately accounts for the Lorentz contraction of the excluded volume of two relativistic hadrons with hard-core repulsion is worked out. Using the obtained expression we heuristically derive the equation of state of Boltzmann particles with relativistic excluded volumes in terms of system pressure and its surface and curvature tension coefficients. The behavior of effective excluded volumes of lightest baryons and mesons is studied at very high temperatures (particle number densities) and for very large values of degeneracy factors. Several parameterizations of the obtained equation of state demonstrate a universal asymptotic of the effective excluded volume at high particle number densities. It is peculiar, that the found maximal packing fraction eta similar or equal to 0.75 eta exc approximate to 0.74