Metastable nematic hedgehogs

For nematic liquid crystals, we study the local stability of a radial hedgehog against biaxial perturbations. Our analysis employs the Landau - de Gennes functional to describe the free energy stored in a ball, whose radius is a parameter of the model. We find that a radial hedgehog may be either unstable or metastable, depending on the values of the elastic constants. For unstable hedgehogs, we give an explicit expression for the radius of the ball within which the instability manifests itself: it can be interpreted as the size of the biaxial core of the defect; it is of the same order of magnitude as the radius of the disclination ring predicted by Penzenstadler and Trebin's model. The metastable hedgehogs predicted by our model are the major novelty of the paper. They tell us that we may also expect truly uniaxial point defects, whose core contains no biaxial structure.