Essentials of Blackfold Dynamics

TL;DR

This paper develops a generalized effective theory for higher-dimensional black holes, modeling them as black branes with a fluid-like description on a dynamical worldvolume, enabling analysis of equilibrium and stability.

Contribution

It introduces a significantly generalized blackfold formalism that combines intrinsic fluid dynamics with extrinsic geometry, facilitating the construction and analysis of complex black hole solutions.

Findings

Derived equilibrium configurations for blackfolds.

Connected Gregory-Laflamme instability to fluid sound modes.

Discussed thermodynamics and extensions of the formalism.

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.