Master field treatment of metric perturbations sourced by the trailing string

TL;DR

This paper derives decoupled, separable linearized Einstein equations for metric perturbations caused by a trailing string in a thermal N=4 super-Yang-Mills background, solving them for large and small wave-numbers.

Contribution

It introduces a novel decoupled and separable formulation of Einstein equations for string-induced perturbations in a holographic setting.

Findings

Explicit solutions for large wave-numbers

Explicit solutions for small wave-numbers

Framework applicable to analyzing string-induced metric perturbations

Abstract

We present decoupled, separable forms of the linearized Einstein equations sourced by a string trailing behind an external quark moving through a thermal state of N=4 super-Yang-Mills theory. We solve these equations in the approximations of large and small wave-numbers.