The Gregory–Laflamme instability

This article reviews the Gregory–Laflamme instability in higher-dimensional general relativity. This is an linear instability, which grows exponentially, that arises when a black hole is sufficiently extended in one direction to support a long wavelength perturbation. When tracked into the non-linear regime there is evidence to suggest that this instability gives rise to a violation of the weak cosmic censorship conjecture. The focus of this article is on how this instability afflicts the Schwarzschild black string and other vacuum black hole solutions.