Nonlinear oscillations of compact stars in the vicinity of the maximum mass configuration

¹ Frankfurt Institute for Advanced Studies (FIAS) - Ruth-Moufang-Straße 1, 60438 Frankfurt am Main, Germany
² Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität - Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
³ Kurchatov Institute, Russian Research Center - Akademika Kurchatova Square, 123182 Moscow, Russian Federation

Received: 4 March 2015
Accepted: 15 July 2015

Abstract

We solve the dynamical GR equations for the spherically symmetric evolution of compact stars in the vicinity of the maximum mass, for which instability sets in according to linear perturbation theory. The calculations are done with the analytical Zeldovich-like EOS and with the TM1 parametrisation of the RMF model. The initial configurations for the dynamical calculations are represented by spherical stars with equilibrium density profile, which are perturbed by either i) an artificially added inward velocity field proportional to the radial coordinate, or ii) a rarefaction corresponding to a static and expanded star. These configurations are evolved using a one-dimensional GR hydro code for ideal and barotropic fluids. Depending on the initial conditions we obtain either stable oscillations or the collapse to a black hole. The minimal amplitude of the perturbation, needed to trigger gravitational collapse is evaluated. The approximate independence of this energy on the type of perturbation is pointed out. At the threshold we find type-I critical behaviour for all stellar models considered and discuss the dependence of the time scaling exponent on the baryon mass and EOS.