A rotating black ring solution in five dimensions.

By Roberto Emparan, Harvey Reall. Physical Review Letters, 2001

866 citations recorded by the source corpus.

The vacuum Einstein equations in five dimensions are shown to admit a solution describing a stationary asymptotically flat spacetime regular on and outside an event horizon of topology S1xS2. It describes a rotating "black ring." This is the first example of a stationary asymptotically flat vacuum solution with an event horizon of nonspherical topology. The existence of this solution implies that the uniqueness theorems valid in four dimensions do not have simple five-dimensional generalizations. It is suggested that increasing the spin of a spherical black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dca680deacfab89d95070be17a5ec712e61ee54a

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Citations in the corpus

The Kerr metric (2014, background): “But in five dimensions there are also the Emparan-Reall black rings with S(2)×S(1) horizon topology [72]; the Pomeransky-Senkov black rings, which have a second angular momentum parameter [73]; and the “Black Saturn” solutions, which are multi-component black holes where a spherical horizon is surro”
Supersymmetric black rings and three-charge supertubes (2004, background): “The metric dx24 (which we shall sometimes refer to as the “base space”) is just the flat metric on E4 written in ‘ring coordinates’ [24, 1 , 2, 3, 5]. These foliate E4 by surfaces of constant y with topology S1 × S2, which are equipotential surfaces of the field created by a ring-like source.”
Topology change in general relativity, and the black-hole black-string transition (2002, background): “The black hole uniqueness theorems (“no hair”), which characterizes a time-independent 4d black hole by its mass and angular momentum (and possibly gauge charges), does not hold as such for d > 4. The 5d rotating black ring solution of [ 48 ] is a beautiful counterexample where for some values of th”
All-genus calculation of Wilson loops using D-branes (2005, methodology): “4 These coordinates have some resemblance to the ones used to describe black rings, see e.g. [ 23 ].”
Stationary and axisymmetric solutions of higher-dimensional general relativity (2004, methodology): “while for c = 1 it has the value 32/(27π). This is in accordance with [ 6 , 22, 20].”
Numerical methods for finding stationary gravitational solutions (2015, background): “By now, there are examples for each of these topologies [332, 336, 342].”