# Non-linear perturbation of black branes at large $D$

## TL;DR

This paper develops a higher-order perturbation theory for black branes in the large-D limit, providing explicit solutions for various initial conditions and exploring phenomena like the Gregory-Laflamme instability.

## Contribution

It introduces a novel higher-order time-domain perturbation framework for black branes, enabling detailed analysis of their dynamic evolution and stability.

## Key findings

- Explicit solutions for black-brane evolution under different initial conditions
- Insights into Gregory-Laflamme instability and non-equilibrium steady states
- Framework applicable to holographic dual field theories

## Abstract

The Einstein equations describing the black-brane dynamics both in Minkowski and AdS background were recently recast in the form of coupled diffusion equations in the large-$D$(imension) limit. Using such results in the literature, we formulate a higher-order perturbation theory of black branes in time domain and present the general form of solutions for arbitrary initial conditions. For illustrative purposes, the solutions up to the first or second order are explicitly written down for several kind of initial conditions, such as a Gaussian wave packet, shock wave, and rather general superposed sinusoidal waves. These could be the first examples describing the non-trivial evolution of black-brane horizons in time domain. In particular, we learn some interesting aspects of black-brane dynamics such as the Gregory-Laflamme (GL) instability and non-equilibrium steady state (NESS). The formalism presented here would be applicable to the analysis of various black branes and their holographically dual field theories.