# Cosmic Censorship Upheld in Spheroidal Collapse of Collisionless Matter

## TL;DR

This study demonstrates that spheroidal collapse of collisionless matter in general relativity results in black hole formation and gravitational radiation, upholding the cosmic censorship conjecture and challenging earlier claims of naked singularities.

## Contribution

Revisits previous spheroidal collapse scenarios with different coordinates and parameters, showing all cases lead to black holes, thus supporting cosmic censorship.

## Key findings

- All configurations studied form black holes with apparent horizons.
- Proper horizon circumferences do not exceed hoop conjecture bounds.
- Strong gravitational radiation emitted during collapse, up to high luminosities.

## 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 $P_{\rm GW}\sim 2\times 10^{-3}c^5/G$.