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 asymptotics of the effective excluded volume at high particle number densities. It is peculiar, that the found maximal packing fraction $eta simeq 0.75$ of Lorentz contracted particles is very close to the dense packing limit of classical hard spheres of same radius $eta_{exc} approx 0.74$. We show that the developed equation of state is the grand canonical formulation of the morphological thermodynamics approach applied to Lorentz contracted rigid spheres.
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