Static solutions of the Einstein-Dirac system for an increasing number of particles behave as solutions of the Einstein- Vlasov system
| dc.contributor.author | Blomqvist, Joakim | |
| dc.contributor.department | Chalmers tekniska högskola / Institutionen för matematiska vetenskaper | sv |
| dc.contributor.examiner | Andréasson, Håkan | |
| dc.contributor.supervisor | Andréasson, Håkan | |
| dc.date.accessioned | 2023-12-01T09:33:38Z | |
| dc.date.available | 2023-12-01T09:33:38Z | |
| dc.date.issued | 2023 | |
| dc.date.submitted | 2023 | |
| dc.description.abstract | In this thesis we will study 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. [10] 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 [14]. 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 very similar. 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 appears to be 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. | |
| dc.identifier.coursecode | MVEX03 | |
| dc.identifier.uri | http://hdl.handle.net/20.500.12380/307418 | |
| dc.setspec.uppsok | PhysicsChemistryMaths | |
| dc.subject | General relativity, relativistic quantum mechanics, phenomenological matter model, field theoretic matter model. | |
| dc.title | Static solutions of the Einstein-Dirac system for an increasing number of particles behave as solutions of the Einstein- Vlasov system | |
| dc.type.degree | Examensarbete för masterexamen | sv |
| dc.type.degree | Master's Thesis | en |
| dc.type.uppsok | H | |
| local.programme | Engineering mathematics and computational science (MPENM), MSc |