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We study the spherical collapse of an over-density of a barotropic fluid withlinear equation of state in a cosmological background. Fully relativisticsimulations are performed by using the Baumgarte-Shibata-Shapiro-Nakamuraformalism jointly with the Valencia formulation of the hydrodynamics. Thispermits us to test the universality of the critical collapse with respect tothe matter type by considering the constant equation of state parameter$\omega$ as a control parameter. We exhibit, for a fixed radial profile of theenergy-density contrast, the existence of a critical value $\omega^*$ for theequation of state parameter under which the fluctuation collapses to a blackhole and above which it is diluting. It is shown numerically that the mass ofthe formed black hole, for subcritical solutions, obeys a scaling law $M\propto|\omega - \omega^*|^\gamma$ with a critical exponent $\gamma$ independent onthe matter type, revealing the universality. This universal scaling law isshown to be verified in the empty Minkoswki and de Sitter space-times. For thefull matter Einstein-de Sitter universe, the universality is not observed ifconformally flat sub-horizon initial conditions are used. But whensuper-horizon initial conditions computed from the long-wavelengthapproximation are used, the universality appears to be true.

Universality of the spherical collapse with respect to the matter type : the case of a barotropic fluid with linear equation of state