Abstract
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.
Highlights
Classical general relativity in more than four spacetime dimensions has been the subject of increasing attention in recent years
The AdS/conformal field theory (CFT) correspondence relates the dynamics of a d-dimensional black hole with those of a quantum field theory in d − 1 dimensions [187]
Four-dimensional black holes are known to have a number of remarkable features, such as uniqueness, spherical topology, dynamical stability, and to satisfy a set of simple laws — the laws of black hole mechanics
Summary
The black-hole uniqueness theorem states that there is at most one stationary, asymptotically-flat, vacuum black-hole solution with given mass and angular momentum: the Kerr black hole. The coexistence of Myers–Perry black holes and black rings shows explicitly that blackhole uniqueness is violated in five dimensions. There is strong evidence that this is even more dramatically true in more than five dimensions. Even if higher-dimensional black holes are not uniquely characterized by their conserved charges, we can still hope to classify them. A major goal of research in higher-dimensional general relativity is to solve the classification problem: determine all stationary, asymptotically-flat black-hole solutions of the higher-dimensional vacuum Einstein equation (or Einstein equation coupled to appropriate matter). We are still a long way from this goal, but partial progress has been made, as we shall review below
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