Critical Collapse of Einstein Cluster

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.Comment: Accepted for publication in Prog. Theor. Phy

Timescale for trans-Planckian collisions in Kerr spacetime

We make a critical comparison between ultra-high energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time required for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years which is much shorter than the age of the Universe. Thus from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black hole counterparts.Comment: 15 pages, v2: minor revisions, v3: minor revisions, to appear in EP

Can inhomogeneties accelerate the cosmic volume expansion?

If expanding and contracting regions coexist in the universe, the speed of the cosmic volume expansion can be accelerated. We construct simple inhomogeneous dust-filled universe models in which the speed of the cosmic volume expansion is accelerated for finite periods. These models are constructed by removing spherical domains from the Einstein-de Sitter universe and filling each domain with a Lemaitre-Tolman-Bondi dust sphere possessing the same gravitational mass as the removed region. This represents an exact solution of the Einstein equations. We find that acceleration of the cosmic volume expansion is realized in some cases when the size of the contracting region is comparable to the horizon radius of the Einstein-de Sitter universe though this model is very different from the universe observed today. This result implies that non-linear general relativistic effects of inhomogeneities are very important to realize the acceleration of the cosmic volume expansion.Comment: 12 pages,5 figures. version published in Progress of Theoretical Physic