Gregory-Laflamme analysis of MGD black strings

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.