MG11 
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Naked singularity formation in the gravitational collapse of an ultrarelativistic fluid.

We numerically investigate the gravitational collapse of a fluid with the equation of state P = k*rho. It has been shown by Ori and Piran (1990) that for k<=0.01 the (self-similar) general relativistic Larson-Penston (GRLP) solutions contains a naked singularity. Harada and Maeda (2001) suggested that GRLP is an attractor in the supercritical regime of a gravitational collapse, and therefore naked singularities can form from a generic initial data. Our calculations confirm that a generic supercritical solution for k<= 0.01 indeed converges to the GRLP. Our numerical code uses high resolution shock capturing methods to evolve the fluid. It incorporates adaptive mesh refinment and all the calculations are done in quadruple precision.