Cosmic hoop conjecture\?

Details Cosmic hoop conjecture\? Cosmic hoop conjecture\?

Oct 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phrvd..50.4903c&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 50, Issue 8, 15 October 1994, pp.4903-4913

Mathematics

Logic

7

Singularities And Cosmic Censorship, Fundamental Problems And General Formalism, Black Holes

Scientific paper

We propose a hoop conjecture in the presence of a positive cosmological constant Λ: when an apparent horizon forms in a gravitational collapse, the matter must be sufficiently compactified such that the circumference scrC satisfies the condition scrC<~4πM<~4πMcrit, where M is the Abbott-Deser mass of the collapsed body and Mcrit=1/3 √Λ . To confirm our conjecture, we investigate two cases: (1) initial data of a prolate or oblate dust spheroid, and (2) the Kastor-Traschen spacetime which describes a black hole collision with Λ. We also discuss a relation between the hoop conjecture and an appearance of a naked singularity.

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