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

TL;DR

This paper presents an analytic derivation of the Schwarzschild black hole's negative mode, crucial for understanding quantum gravity and black string instabilities, using a novel gauge fixing approach and generalizing to other geometries.

Contribution

It introduces a new analytic method for deriving the black hole negative mode by postponing gauge fixing and leveraging the action's properties, extending to broader geometries.

Findings

Analytic derivation of the Schwarzschild negative mode.

Generalization to perturbations around co-homogeneity 1 geometries.

Enhanced understanding of black hole stability and quantum gravity implications.

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.