World-Volume Effective Theory for Higher-Dimensional Black Holes

TL;DR

The authors address the rich dynamics of higher-dimensional black holes by introducing the blackfold worldvolume theory, which captures long-distance behavior when two horizon scales are widely separated ($r_0\ll R$). By treating the hole as a boosted black $p$-brane wrapped on a submanifold, they derive effective equations from conserved stress-energy and extrinsic curvature balance, enabling explicit solutions such as products of odd-spheres and ultraspinning Myers–Perry limits. The framework explains novel horizon geometries and topologies, provides a unified method to compute global charges and horizon area, and suggests avenues for generalizations to charged or non-Minkowski backgrounds. Overall, it offers a principled, scalable approach to organize and explore the diverse landscape of higher-dimensional black holes beyond four dimensions.

Abstract

We argue that the main feature behind novel properties of higher-dimensional black holes, compared to four-dimensional ones, is that their horizons can have two characteristic lengths of very different size. We develop a long-distance worldvolume effective theory that captures the black hole dynamics at scales much larger than the short scale. In this limit the black hole is regarded as a blackfold: a black brane (possibly boosted locally) whose worldvolume spans a curved submanifold of the spacetime. This approach reveals black objects with novel horizon geometries and topologies more complex than the black ring, but more generally it provides a new organizing framework for the dynamics of higher-dimensional black holes.