Hoop conjecture for colliding black holes

Details Hoop conjecture for colliding black holes Hoop conjecture for colliding black holes

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phrvd..58l1501i&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 58, Issue 12, 15 December 1998, id. 121501

Physics

13

Classical Black Holes

Scientific paper

We study the collision of black holes in the Kastor-Traschen space-time, at present the only such analytic solution. We investigate the dynamics of the event horizon in the case of the collision of two equal black holes, using the ray-tracing method. We confirm that the event horizon has trouser topology and show that its set of past end points (where the horizon is nonsmooth) is a spacelike curve resembling a seam of trousers. We show that this seam has a finite length and argue that twice this length be taken to define the minimal circumference C of the event horizon. Comparing with the asymptotic mass M, we find the inequality C<4πM supposed by the hoop conjecture, with both sides being of similar order, C~4πM. This supports the hoop conjecture as a guide to general gravitational collapse, even in the extreme case of head-on black-hole collisions.

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