Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow

A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.Comment: 9 pages, 11 figures; v2: references added, typos corrected; v3: accepted for publication in Physical Review

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