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arXiv · gr-qc/0302058

Hoop Conjecture and Black Holes on a Brane

Kouji Nakamura·Ken-ichi Nakao·Takeshi Mishima
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Abstract

The initial data of gravity for a cylindrical matter distribution confined to a brane are studied in the framework of the single-brane Randall-Sundrum scenario. In this scenario, the 5-dimensional nature of gravity appears in the short-range gravitational interaction. We find that a sufficiently thin configuration of matter leads to the formation of a marginal surface, even if the configuration is infinitely long. This implies that the hoop conjecture proposed by Thorne does not hold on the brane: Even if a mass $M$ does not become compacted into a region whose circumference ${\cal C}$ in every direction satisfies ${\cal C}> 4πGM$, black holes with horizons can form in the Randall-Sundrum scenario.

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Kouji Nakamura, Ken-ichi Nakao, Takeshi Mishima. 2003-02-14. Hoop Conjecture and Black Holes on a Brane. https://doi.org/10.1143/ptps.148.291

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