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We develop the effective worldvolume theory for the dynamics of black branes with charges of the kind that arise in many supergravities and low-energy limits of string theory. Using this theory, we construct numerous new rotating black holes with charges and dipoles of D-branes, fundamental strings and other branes. In some instances, the black holes can be dynamically stable close enough to extremality. Some of these black holes, such as those based on the D1-D5-P system, have extremal, non-supersymmetric limits with regular horizons of finite area and a wide variety of horizon topologies and geometries.

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