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 $\mathcal{S}[\mathcal{\eta }]$ 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 $m(r)\mathrm{/}r$ 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.