The Power of Action: "The" Derivation of the Black Hole Negative Mode

Abstract

The negative mode of the Schwarzschild black hole is central to Euclidean quantum gravity around hot flat space and for the Gregory-Laflamme black string instability. Numerous gauges were employed in the past to analyze it. Here _the_ analytic derivation is found, based on postponing the gauge fixing, on the power of the action and on decoupling of non-dynamic fields. A broad-range generalization to perturbations around arbitrary co-homogeneity 1 geometries is discussed.