Derivation of the blackfold effective theory

TL;DR

This work derives the blackfold effective theory from first-principles Einstein gravity for long-wavelength perturbations of neutral black p-branes, showing intrinsic (fluid-like) and extrinsic (elastic) fluctuations decouple at leading order. The authors construct adapted Fermi-like coordinates, solve the perturbed Einstein equations, and prove horizon regularity, yielding explicit near-brane geometries to leading derivative order. They present a covariant complete metric incorporating both fluid and extrinsic corrections, along with the governing blackfold equations for $r_0$, $u^a$, and $K_{ab}{}^i$. The results provide an ab initio foundation for the blackfold approach, with clear pathways to extensions to charged branes, AdS/CFT contexts, and higher-derivative corrections, thereby enabling systematic exploration of new higher-dimensional black holes and their stability.

Abstract

We study fluctuations and deformations of black branes over length scales larger than the horizon radius. We prove that the Einstein equations for the perturbed p-brane yield, as constraints, the equations of the effective blackfold theory. We solve the Einstein equations for the perturbed geometry and show that it remains regular on and outside the black brane horizon. This study provides an ab initio derivation of the blackfold effective theory and gives explicit expressions for the metrics near the new black holes and black branes that result from it, to leading order in a derivative expansion.