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The Hoop Conjecture for Black Rings · Around

2012

The Hoop Conjecture for Black Rings

Mujtaba, A. H., Pope, C. N.

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A precise formulation of the hoop conjecture for four-dimensional spacetimes proposes that the Birkhoff invariant \beta for an apparent horizon in a spacetime with mass M should satisfy \beta \le 4\pi M.

The invariant \beta is the least maximal length of any sweepout of the 2-sphere apparent horizon by circles.
An analogous conjecture in five spacetime dimensions was recently formulated, asserting that the Birkhoff invariant \beta for S^1\times S^1 sweepouts of the apparent horizon should satisfy \beta \le (16/3)\pi M.
Although this hoop inequality was formulated for conventional five-dimensional black holes with 3-sphere horizons, we show here that it is also obeyed by a wide variety of black rings, where the horizon instead has S^2\times S^1 topology.

Built on

K.S. Thorne, Nonspherical gravitational collapse: A short review
1972
Earlier work this paper cites.
M. Cvetič and D. Youm, General rotating five-dimensional black holes of toroidally compactified heterotic string
1996
Earlier work this paper cites.
R. Emparan and H.S. Reall, A rotating black ring in five dimensions
2002
Earlier work this paper cites.
H. Elvang, A charged rotating black ring
2003
Earlier work this paper cites.

Similar

R. Emparan, Rotating circular strings, and infinite nonuniqueness of black rings
2004
Cited alongside, same era.
Z.-W. Chong, M. Cvetič, H. Lü and C.N. Pope, General non-extremal rotating black holes in minimal five-dimensional gauged supergravity
2005
Cited alongside, same era.
R. Emparan and H.S. Reall, Black rings
2006
Cited alongside, same era.
G.W. Gibbons, Birkhoff’s invariant and Thorne’s hoop conjecture
Original
Cited in the paper.
A.A. Pomeransky and R.A. Sen’kov, Black ring with two angular momenta
Cited in the paper.

Then

J. Hoskisson, A charged boubly spinning black ring
Original
2009
Later among the works it cites.
D.V. Gal’tsov and N.G. Scherbluk, Three-charge doubly rotating black ring
Original
2010
Later among the works it cites.
M. Cvetič, G.W. Gibbons and C.N. Pope, More about Birkhoff’s invariant and Thorne’s hoop conjecture for horizons
Original
2011
Later among the works it cites.

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