Gregory-Laflamme analysis of MGD black strings

TL;DR

This paper investigates the stability of MGD black strings by analyzing their perturbations via the Gregory-Laflamme instability, revealing a critical mass threshold for stability and connecting 4D solutions with Ricci quadratic gravity.

Contribution

It demonstrates that MGD black strings' stability can be understood through Lichnerowicz eigenmodes, identifying a critical mass for stability and linking 4D Ricci quadratic gravity to black string perturbations.

Findings

Existence of a critical mass for MGD black string stability

MGD black strings are stable above the critical mass

Standard GR black strings are unstable, consistent with Gregory-Laflamme instability

Abstract

The minimal geometric deformation (MGD), associated with the 4D Schwarzschild solution of the Einstein equations, is shown to be a solution of the pure 4D Ricci quadratic gravity theory, whose linear perturbations are then implemented by the Gregory-Laflamme eigentensors of the Lichnerowicz operator. The stability of MGD black strings is hence studied, through the correspondence between their Lichnerowicz eigenmodes and the ones associated with the 4D MGD solutions. Its is shown that there exists a critical mass driving the MGD black strings stability, above which the MGD black string is precluded from any Gregory-Laflamme instability. The general relativistic limit leads the MGD black string to be unstable, as expected, corresponding to the standard Gregory-Laflamme black string instability.