STIFFNESS, COMPLEXITY, CRACKING AND STABILITY OF RELATIVISTIC COMPACTS STARS

The compactness of a relativistic compact star provides an essential clue to the matter composition of the star. In this paper, we explore many versions of the Tolman VII solution to analyse the maximum compactness of a relativistic star in the context of a given equation of state (EOS). For an EOS specified by the model parameters in the Tolman VII solution, we evaluate the critical bound on compactness above which the stellar composition becomes unstable against radial oscillations. We also outline the possible link between stellar stability, 'complexity', and 'cracking' of an anisotropic stellar configuration.