Perturbed hedgehogs: continuous deformation of point defects in biaxial nematic liquid crystals

Abstract

A spherically symmetric isolated point defect in a 3D uniaxial nematic liquid crystal sample is often called a {\it radial hedgehog}. We use topological methods to describe local configurations of uniaxial and biaxial states into which a hedgehog naturally deforms under small perturbations: these include the biaxial torus and split core configurations studied in the literature using analytical and numerical methods. The topological results here take no account of the governing physical laws but provide a library of options from which the physics must make a choice.