Princeton University Gravity Initiative Fall Seminar Series

The Gregory--Laflamme Instability of the 5D Schwarzschild Black String Exterior

Abstract: I will discuss a direct rigorous mathematical proof of the Gregory--Laflamme instability for the 5D Schwarzschild black string. This is a mode instability at the level of the linearised vacuum Einstein equation. Under a choice of ansatz for the perturbation and a gauge choice, the linearised vacuum Einstein equation can be reduced to a Schrödinger eigenvalue equation to which an energy functional is assigned. It is then shown by direct variational methods that the lowest eigenfunction gives rise to an exponentially growing mode solution which has admissible behaviour at the future event horizon and spacelike infinity in harmonic/transverse-traceless gauge.

Date & Time

November 07, 2022 | 12:30pm – 1:30pm


Princeton University, Jadwin Hall, Princeton Gravity Initiative, 4th Floor & Zoom


Sam Collingbourne


Columbia University