Oscillations of compact stars evolving towards the point of gravitational instability

A significant portion of compact objects will collapse to form black holes, e.g., a proto-neutron star with mass larger than the maximum mass the equation of state (EOS) can support at zero temperature will eventually collapse upon neutrino cooling or other dissipative processes. We found that in the cooling process the fundamental oscillation frequency. would first rise to a peak value shortly before it drops abruptly to zero at the instability point, quite independent of the specific choice of the EOS and cooling mechanism. The rapidity of the drop gives a clear signal that a gravitational collapse is imminent.