Essentials of Blackfold Dynamics

TL;DR

This work develops a comprehensive effective worldvolume theory for higher-dimensional black holes by modeling a black hole as a curved boosted black brane (a blackfold) with a fluid living on a dynamical worldvolume. It splits the dynamics into intrinsic (fluid) and extrinsic (embedding) equations, enabling efficient construction of stationary black holes and analysis of time evolution, including the long-wavelength Gregory-Laflamme instability as a sound-mode instability. The framework uses Brown-York quasilocal stress tensors and matched asymptotic expansions to connect near-horizon and asymptotic regions, deriving horizon thermodynamics, a first-law structure, and an embedding action for stationary configurations. It also links to the membrane paradigm and fluid/AdS-gravity correspondence, providing a versatile platform for extensions to non-vacuum and charged backgrounds and for exploring higher-derivative corrections.

Abstract

We develop and significantly generalize the effective worldvolume theory for higher-dimensional black holes recently proposed by the authors. The theory, which regards the black hole as a black brane curved into a submanifold of a background spacetime -a blackfold-, can be formulated in terms of an effective fluid that lives on a dynamical worldvolume. Thus the blackfold equations split into intrinsic (fluid-dynamical) equations, and extrinsic (generalized geodesic embedding) equations. The intrinsic equations can be easily solved for equilibrium configurations, thus providing an efficient formalism for the approximate construction of novel stationary black holes. Furthermore, it is possible to study time evolution. In particular, the long-wavelength component of the Gregory-Laflamme instability of black branes is obtained as a sound-mode instability of the effective fluid. We also discuss action principles, connections to black hole thermodynamics, and other consequences and possible extensions of the approach. Finally, we outline how the fluid/AdS-gravity correspondence is related to this formalism.