Cosmic Censorship Upheld in Spheroidal Collapse of Collisionless Matter

Abstract

We study the collapse of spheroidal configurations of collisionless particles in full general relativity. This setup was originally considered by Shapiro and Teukolsky (1991), where it was found that prolate configurations with a sufficiently large semimajor axis gave rise to diverging curvature, but no apparent horizon. This was taken as evidence for the formation of a naked singularity, in violation of cosmic censorship. We revisit such configurations using different coordinates/slicing, and considering a range of values for the semimajor axis and eccentricity of the initial matter distribution, and find that the final state in all cases studied is a black hole plus gravitational radiation. Though initially distorted, the proper circumferences of the apparent horizons that are found do not significantly exceed the hoop conjecture bound. Configurations with a larger semimajor axis can produce strong gravitational radiation, with luminosities up to $P_{\mathrm{GW}}\sim 2\times 10^{-3}{c}^5/G$.

arXiv comment6 pages, 6 figures; revised to match PRL version, including expanded results

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• Numerical solutions to Einstein's equations in a shearing-dust Universe: a code comparison
• Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture
• General Relativistic Cosmological N-body Simulations I: time integration
• Einstein-Vlasov Calculations of Structure Formation
• On the Hoop conjecture and the weak cosmic censorship conjecture for the axisymmetric Einstein-Vlasov system
• Introducing the inverse hoop conjecture for black holes
• Cylindrical spacetimes due to radial magnetic fields
• Dynamics of gravitational collapse in the axisymmetric Einstein-Vlasov system