Quadrupole Instabilities of Relativistic Rotating Membranes

TL;DR

This paper investigates the stability of relativistic rotating membranes, revealing that while some deformations are stable, higher spin quadrupole deformations cause instabilities leading to decay into finger-like shapes.

Contribution

It extends previous stability analysis from spherical to ellipsoidal membranes, identifying specific unstable modes for higher spin deformations.

Findings

Quadrupole and higher spin deformations induce instabilities.

Ellipsoidal membranes tend to decay into finger-like configurations.

Stability persists only for spin l=1 deformations.

Abstract

We generalize recent study of the stability of isotropic (spherical) rotating membranes to the anisotropic ellipsoidal membrane. We find that while the stability persists for deformations of spin $l=1$, the quadrupole and higher spin deformations ($l\geq 2$) lead to instabilities. We find the relevant instability modes and the corresponding eigenvalues. These indicate that the ellipsoidal rotating membranes generically decay into finger-like configurations.