The Role of Angular Momentum and Cosmic Censorship in the (2+1)-Dimensional Rotating Shell Collapse

Abstract

We study the gravitational collapse problem of rotating shells in three-dimensional Einstein gravity with and without a cosmological constant. Taking the exterior and interior metrics to be those of stationary metrics with asymptotically constant curvature, we solve the equations of motion for the shells from the Darmois-Israel junction conditions in the "co-rotating" frame. We study various collapse scenarios with "arbitrary" angular momentum for a variety of geometric configurations, including anti-de Sitter, de Sitter, and flat spaces. We find that the collapsing shells can form a BTZ black hole, a three-dimensional Kerr-dS spacetime, and an horizonless geometry of point masses under certain initial conditions. For pressureless dust shells, the curvature singularity is "not" formed due to the angular momentum barrier near the origin. However when the shell pressure is nonvanishing, we find that for all types of shells with polytropic-type equations of state (including the perfect fluid and the generalized Chaplygin gas), collapse to a naked singularity is "possible" under generic initial conditions. We conclude that in three dimensions angular momentum does not in general guard against violation of cosmic censorship.

arXiv commentAdded Comments on a caveat of three dimensions and the critical behavior (p.26); Added References; Accepted in PRD

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