Gravity thaws the frozen moduli of the CP^1 lump

TL;DR

This paper studies how gravity influences the dynamics of CP^1 lumps, revealing that gravitational effects can cause previously fixed moduli to vary and lead to instability of these lumps.

Contribution

It provides explicit metrics for the moduli space of self-gravitating CP^1 lumps and analyzes their stability under gravitational effects.

Findings

Gravity causes moduli to become dynamic, unlike in the non-gravitational case.

Strong gravity shrinks physical space and affects boundary conditions.

Weak coupling moduli space is geodesically incomplete, indicating instability.

Abstract

The slow motion of a self-gravitating CP^1 lump is investigated in the approximation of geodesic flow on the moduli space of unit degree static solutions M_1. It is found that moduli which are frozen in the absence of gravity, parametrizing the lump's width and internal orientation, may vary once gravitational effects are included. If gravitational coupling is sufficiently strong, the presence of the lump shrinks physical space to finite volume, and the moduli determining the boundary value of the CP^1 field thaw also. Explicit formulae for the metric on M_1 are found in both the weak and strong coupling regimes. The geodesic problem for weak coupling is studied in detail, and it is shown that M_1 is geodesically incomplete. This leads to the prediction that self-gravitating lumps are unstable.