Derivation of the blackfold effective theory

TL;DR

This paper derives the blackfold effective theory from Einstein equations, providing explicit metric expressions for perturbed black branes and demonstrating their regularity, thus offering a fundamental understanding of black brane dynamics.

Contribution

It offers the first ab initio derivation of the blackfold effective theory directly from Einstein equations, including explicit metric solutions.

Findings

Effective blackfold equations are derived as constraints from Einstein equations.

Perturbed black brane geometries remain regular outside the horizon.

Explicit metric expressions near black holes and branes are obtained.

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.