Gravity thaws the frozen moduli of the CP¹ lump

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.