For black holes, researchers know what to expect. The collision of two black holes causes gravitational waves. For neutron stars the question is more subtle, Luciano Rezzolla explained. The collision of two neutron stars leads to an hyper-massive neutron star and an unknown phenomenon. The ejected matter undergoes a nucleosynthesis of heavy elements.
Researchers try to perform a realistic modelling of the two-body problem. Einstein's theory is as beautiful as it is intractable analytically. Researchers are using a series of methods. The Einstein equations are highly nonlinear but involve smooth functions which express as first-order in time, and second order in space non-conservative form. Things are complicated by the formation of strong shocks or black holes, Luciano Rezzolla told the audience.
A whole set of more than 30 PDEs evolved in time with the Method of Lines. The beauty of equations is lost when moving away from tensor notation. These equations are known as a first-order conformal covariant Z4 formulation of the Einstein equations.
The merger of two neutron stars leads to an hyper-massive neutron star (HMNS) amounting in a black hole and torus. Quantitative differences are produced by the total mass when comaring a prompt versus a delayed collapse. There are mass asymmetries for the HMNS and the torus. Soft and stiff EOS are observed during the inspiral and post-merger period. Researchers also observe magnetic fields and radiative losses. The question rises how to constrain the EOS, Luciano Rezzolla showed.
How do you distinguish a binary neutron star from a black hole? A binary neutron star has a chirp signal at the beginning, something in between and then a ringdown. A black hole has a chirp signal at the start and a ringdown afterwards. Soft EOS is defined by a high frequency signal and stiff EOS by a low frequency signal. There are also lines, logically not different from emission lines from stellar atmospheres.
Luciano Rezzolla explained about the new approach to constrain the EOS by constraining the radius via semi-analytical modelling and MC analysis. The very soft EOSs remain a challenge. Discriminating two-stiff and two-soft EOSs will be harder.
Since the seventies of the past century, researchers have observed flashes of gamma rays with enormous energies. There are two families of bursts: long and short. The first ones last tens or more of seconds and could be due to the collapse.
Luciano Rezzolla concluded that the missing link between theory and observation is found thanks to HPC. The spectra of post-merger events show peaks, some quasi-universal. When used together with tens of observations, they will set tight constraints on EOS. The radius is known with 1 km precision. Magnetic fields are unlikely to be detected during the inspiral but are important after the merger. There are instabilities and EM counterparts. Mergers lead to tiny but important ejected matter and macronova emission. The high-A nucleosynthesis is very robust.