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Critical Collapse of Einstein Cluster

By Ashutosh Mahajan, Tomohiro Harada, Pankaj Joshi and Ken-ichi Nakao


We observe critical phenomena in spherically symmetric gravitational collapse of Einstein Cluster. We show analytically that the collapse evolution ends either in formation of a black hole or in dispersal depending on the values of initial parameters which characterize initial density and angular momentum of the collapsing cloud. Near the threshold of black hole formation, we obtain scaling relation for the mass of the black hole and find the critical exponent value to be 3/2. We numerically confirm that there exist wide ranges of initial parameter values around the critical configuration for which the model remains shell-crossing free. Critical behavior in gravitational collapse was first found by Choptuik in nu-merical simulations of spherically symmetric massless scalar field.1) For marginally supercritical data, it was found that the black hole mass scales as M ∼ (p − p∗)γ, where p is a parameter of family of the initial data which characterizes strength o

Year: 2007
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