Speaker
Håkan Andréasson, University of Gothenburg
Abstract
Static spherically symmetric solutions to the Einstein-Dirac system were constructed numerically for the first time in 1999 by Finster et al. in the case of two fermions. In 2020 this result was generalized by Leith et al. to a system consisting of an even number \(\kappa\) of fermions. They constructed solutions for \(2\leq\kappa\leq 90\). The purpose of my talk is to compare the properties of static solutions of the Einstein-Dirac system with static solutions of the Einstein,-Vlasov system as the number of fermions increases, that is, for \(2\leq\kappa \leq 180\). Since the Einstein-Vlasov system is a fully classical physical model, whereas the Einstein-Dirac system is semiclassical and thus has a quantum signature, this framework provides an excellent opportunity to study the transition from quantum to classical behaviour. It turns out that even for a comparatively small number of particles, the features of the solutions are remarkably similar. One property of the solutions that I will discuss is the sign of the radial pressure. For small values of \(\kappa\), there are regions where the radial pressure is negative. These regions disappear as \(\kappa\) increases. This supports the interpretation as a transition from quantum to classical behaviour as the number of fermions increases. The talk is based on a joint work with Joakim Blomqvist.