Massive stars which have burnt their nuclear fuel will collapse under the pull of their gravitational self attraction, sometimes triggering a supernova event. This collapse can lead to situations in which significant gravitational radiation is produced. In particular, there are various scenarios in which the collapsing core is thought to ``hang-up'' in a non-axisymmetric configuration and radiate this assymmetry away through gravitational waves.
A promising scenario of this type was explored by Lai and Shapiro [42] and proceeds as follows:a stellar core with some initial angular momentum collapses. As the collapse proceeds, the ratio of the rotational energy () to the gravitational potential energy () will vary inversely with the core radius. If becomes large enough, the evolution of non-axisymmetric modes of the core become unstable. Such instabilities are well known, being first described by Chandrasekhar [43]. There are two possibilities. If lies in a critical band of values between and , the non-axisymmetric bar mode () of the core will be secularly unstable and grow due to either radiation reaction or viscosity. This long lasting instability is expected to produce significant gravitational radiation. If exceeds the upper limit of this band () then non-axisymmetric modes become dynamically unstable. The transition through dynamical instability is rapid and results in a nearly axisymmetric configuration with but still much larger than . The core therefore again enters the regime of secular instability. In either scenario the onset of the secular instability occurs at approximately neutron star densities. If for the entire collapse, then no significant gravitational radiation is expected from this mechanism.
Lai and Shapiro have calculated the waveform of the gravitational
radiation emitted by a secularly unstable core based on crude Newtonian fluid
ellipsoids models without viscosity. They find [44]: