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This Chapter contains a review of many important aspects of modern black hole theory and its applications. It begins with a general definition of a (not‐necessary stationary) black hole and formulation of the most important results on generic properties of black holes, including the Penrose theorem on the structure of the event horizon, the Hawking theorems on the topology and area of the event horizon and black hole uniqueness theorems. Gravitational radiation from black holes in a binary system and modern status and perspectives of the gravitation waves search from black holes and other compact sources are discussed. We also describe black hole models proposed for the explanation of the gamma‐ray bursts. Modeling of black hole properties, in particular their Hawking radiation, in the laboratory experiments is reviewed. We also discuss recent models with large extra dimensions and possibility of micro black hole creation in the collider experiments. This subject is directly connected with the problem of the higher dimensional black holes. Higher dimensional generalization of the Kerr metric, and a variety of new exact solutions for higher dimensional black objects with the non‐spherical topology of the horizon are discussed. The Chapter ends with remarks on two closely related problems on the wormhole and ‘time machine’ existence. It is shown that in order to create and support macroscopic objects of this type a new exotic form of the matter is requires. It seams that this and possible instabilities make the existence of such objects questionable at least at the present state of our knowledge. These and other fascinating open problems are still wait for their solution.

In previous chapters we presented the key notions associated with stationary black-hole spacetimes, as well as the minimal set of metrics needed to illustrate the basic features of the world of black holes. In this chapter we present some further black holes, selected because of their physical and mathematical interest. We start, in Section 5.1, with the Kerr–de Sitter/anti-de Sitter metrics, the cosmological counterparts of the Kerr metrics. Section 5.2 contains a description of the Kerr–Newman–de Sitter/anti-de Sitter metrics, which are the charged relatives of the metrics presented in Section 5.1. In Section 5.3 we analyse in detail the global structure of the Emparan–Reall ‘black rings’: these are five-dimensional black-hole spacetimes with R × S₁ × S₂-horizon topology. The Rasheed metrics of Section 5.4 provide an example of black holes arising in Kaluza–Klein theories. The Birmingham family of metrics, presented in Section 5.5, forms the most general class known of explicit static vacuum metrics with cosmological constant in all dimensions, with a wide range of horizon topologies.