Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid

We observe critical phenomena in spherical collapse of radiation fluid. A sequence of spacetimes $\cal{S}[\eta]$ is numerically computed, containing models ($\eta\ll 1$) that adiabatically disperse and models ($\eta\gg 1$) that form a black hole. Near the critical point ($\eta_c$), evolutions develop a self-similar region within which collapse is balanced by a strong, inward-moving rarefaction wave that holds $m(r)/r$ constant as a function of a self-similar coordinate $\xi$. The self-similar solution is known and we show near-critical evolutions asymptotically approaching it. A critical exponent $\beta \simeq 0.36$ is found for supercritical ($\eta>\eta_c$) models.