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 S 1 3 S 2 . 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. Black holes in four spacetime dimensions are highly constrained objects. A number of classical theorems show that a stationary, asymptotically flat, vacuum black hole is completely characterized by its mass and spin [1], and event horizons of nonspherical topology are forbidden [2].In this Letter we show explicitly that in five dimensions the situation cannot be so simple by exhibiting an asymptotically flat, stationary, vacuum solution with a horizon of topology S 1 3 S 2 : a black ring. The ring rotates along the S 1 and this balances its gravitational self-attraction. The solution is characterized by its mass M and spin J. The black hole of [3] with rotation in a single plane (and horizon of topology S 3 ) can be obtained as a branch of the same family of solutions. We show that there exist black holes and black rings with the same values of M and J. They can be distinguished by their topology and by their mass dipole measured at infinity. This shows that there is no obvious fivedimensional analog of the uniqueness theorems.S 1 3 S 2 is one of the few possible topologies for the event horizon in five dimensions that was not ruled out by the analysis in [4] (although this argument does not apply directly to our black ring because it assumes time symmetry). An explicit solution with a regular (but degenerate) horizon of topology S 1 3 S 2 and spacelike infinity with S 3 topology has been built recently in [5]. An uncharged static black ring solution is presented in [6], but it contains conical singularities. Our solution is the first asymptotically flat vacuum solution that is completely regular on and outside an event horizon of nonspherical topology.Our starting point is the following metric, constructed as a Wick-rotated version of a solution in [7]:

All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the Gödel universe which lifts to a solution of eleven dimensional supergravity that preserves 20 supersymmetries.

We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.

Gravitational collapse of matter trapped on a brane will produce a black hole on the brane. We discuss such black holes in the models of Randall and Sundrum where our universe is viewed as a domain wall in five-dimensional anti-de Sitter space. We present evidence that a non-rotating uncharged black hole on the domain wall is described by a ''black cigar'' solution in five dimensions.

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl's construction is generalized here to arbitrary dimension Dу4. The general solution of the D-dimensional vacuum Einstein equations that admits DϪ2 orthogonal commuting non-null Killing vector fields is given either in terms of DϪ3 independent axisymmetric solutions of Laplace's equation in threedimensional flat space or by DϪ4 independent solutions of Laplace's equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat ''black ring'' with an event horizon of topology S 1 ϫS 2 held in equilibrium by a conical singularity in the form of a disk.