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We solve the dynamical GR equations for the spherically symmetric evolutionof compact stars in the vicinity of the maximum mass, for which instabilitysets in according to linear perturbation theory. The calculations are done withthe analytical Zeldovich-like EOS P=a(rho-rho_0) and with the TM1parametrisation of the RMF model. The initial configurations for the dynamicalcalculations are represented by spherical stars with equilibrium densityprofile, which are perturbed by either (i) an artificially added inwardvelocity field proportional to the radial coordinate, or (ii) a rarefactioncorresponding to a static and expanded star. These configurations are evolvedusing a one-dimensional GR hydro code for ideal and barotropic fluids.Depending on the initial conditions we obtain either stable oscillations or thecollapse to a black hole. The minimal amplitude of the perturbation, needed totrigger gravitational collapse is evaluated. The approximate independence ofthis energy on the type of perturbation is pointed out. At the threshold wefind type I critical behaviour for all stellar models considered and discussthe dependence of the time scaling exponent on the baryon mass and EOS.

Nonlinear oscillations of compact stars in the vicinity of the maximum mass configuration