We study the spherical collapse of an over-density of a barotropic fluid with linear equation of state in a cosmological background. Fully relativistic simulations are performed by using the Baumgarte–Shibata–Shapiro–Nakamura formalism jointly with the Valencia formulation of the hydrodynamics. This permits us to test the universality of the critical collapse with respect to the matter type by considering the constant equation of state parameter \(\omega \) as a control parameter. We exhibit, for a fixed radial profile of the energy-density contrast, the existence of a critical value \(\omega ^*\) for the equation of state parameter under which the fluctuation collapses to a black hole and above which it is diluting. It is shown numerically that the mass of the formed black hole, for subcritical solutions, obeys a scaling law \(M\propto |\omega - \omega ^*|^\gamma \) with a critical exponent \(\gamma \) independent on the matter type, revealing the universality. This universal scaling law is shown to be verified in the empty Minkoswki and de Sitter space-times. For the full matter Einstein-de Sitter universe, the universality is not observed if conformally flat sub-horizon initial conditions are used. But when super-horizon initial conditions computed from the long-wavelength approximation are used, the universality appears to be true.

我们用宇宙学背景下的线性状态方程研究了正压流体超密度的球形塌陷。完全相对论模拟是通过使用Baumgarte–Shibata–Shapiro–Nakamura形式主义以及瓦伦西亚的水动力公式进行的。这使我们能够通过将状态参数\（\ omega \）的常数方程式作为控制参数，来测试关于物质类型的临界坍塌的普遍性。对于能量密度对比的固定径向轮廓，我们展示出临界值\（\ omega ^ * \）的存在对于状态方程，在该状态方程中，波动崩溃为黑洞，并且在该状态方程上方被稀释。从数值上显示，对于次临界解，形成的黑洞的质量服从具有临界指数\（\ gamma \）的缩放定律\（M \ propto | \ omega-\ omega ^ * | ^ \ gamma \）独立于物质类型，揭示了普遍性。该通用缩放定律在空的Minkoswki和de Sitter时空中已得到验证。对于全物质爱因斯坦-德·西特宇宙，如果使用保形平坦的次地平线初始条件，则不会观察到普遍性。但是，当使用从长波长近似计算得出的超水平初始条件时，通用性似乎是正确的。