Evidence for a gravitational Myers effect

TL;DR

This paper investigates the gravitational Myers effect by analyzing tachyonic modes in non-abelian D0-brane fluctuations, revealing a geometric interpretation linked to curvature and demonstrating the effect in curved spaces and near black hole horizons.

Contribution

It provides a geometric interpretation of the Myers effect through eigenvalues of the geodesic deviation operator and confirms the effect in curved geometries like spheres, hyperboloids, and near black hole horizons.

Findings

Tachyonic modes indicate a gravitational Myers effect in negative curvature regions.

The effect is stable on a sphere but unstable on a hyperboloid.

Near black hole horizons, tachyonic modes suggest a gravitationally induced Myers effect.

Abstract

An indication for the existence of a collective Myers solution in the non-abelian D0-brane Born-Infeld action is the presence of a tachyonic mode in fluctuations around the standard diagonal background. We show that this computation for non-abelian D0-branes in curved space has the geometric interpretation of computing the eigenvalues of the geodesic deviation operator for U(N)-valued coordinates. On general grounds one therefore expects a geometric Myers effect in regions of sufficiently negative curvature. We confirm this by explicit computations for non-abelian D0-branes on a sphere and a hyperboloid. For the former the diagonal solution is stable, but not so for the latter. We conclude by showing that near the horizon of a Schwarzschild black hole one also finds a tachyonic mode in the fluctuation spectrum, signaling the possibility of a near-horizon gravitationally induced Myers effect.