Master's Thesis presentation, Joakim Blomqvist

Abstract: I have studied static solutions to the spherically symmetric Einstein-Dirac system. This system couples Einstein's theory of general relativity to Dirac's relativistic description of quantum mechanics. The goal was to study the transition from a quantum mechanical description to a classical description by comparing properties of the solutions to the Einstein-Dirac system to solutions of the Einstein-Vlasov system as the number of particles of the former system increases. In 1999 Finster et al. found for the first-time static solutions to the Einstein-Dirac system in the case of two fermions with opposite spins. Recently this study has been extended to a larger number of particles by Leith et al.

In particular, they construct highly relativistic solutions. The structure of the solutions is strikingly similar to the structure of highly relativistic solutions of the Einstein-Vlasov system. In both cases multi-peak solutions are obtained, and moreover, the maximum compactness of the solutions is the same. The compactness is measured by the quantity m/r, where m is the mass and r the areal radius, and in both cases the maximum value is 4/9. Furthermore, in quantum mechanics the pressure may be negative whereas classically it is non-negative. We find that already for 16 particles the pressure is non-negative and thus behaves classically. In order to compare the solutions, I need to construct solutions numerically to the Einstein-Dirac system in the case of a large number of particles. This requires a delicate procedure with significant numerical precision when the number of particles in the system grows.

Supervisor: Håkan Andréasson