Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04167 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916933646942208 |
|---|---|
| author | Zhao, Peng Wu, Xiaoning |
| author_facet | Zhao, Peng Wu, Xiaoning |
| contents | In this paper, we investigate the characteristic initial value problem for the Einstein-Dirac system, a model governing the interaction between gravity and spin-$1/2$ fields. We apply Luk's strategy \cite{Luk12} and prove a semi-global existence result for this coupled Einstein-Dirac system without imposing symmetry conditions. More precisely, we construct smooth solutions in a rectangular region to the future of two intersecting null hypersurfaces, on which characteristic initial data are specified. The key novelty is to promote the symmetric spinorial derivatives of the Dirac field to independent variables and to derive a commuted "Weyl-curvature-free" evolution system for them. This eliminates the coupling to the curvature in the energy estimates and closes the bootstrap at the optimal derivative levels. The analysis relies on a double null foliation and incorporates spinor-specific techniques essential to handling the structure of the Dirac field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the local existence for the characteristic initial value problem for the Einstein-Dirac system Zhao, Peng Wu, Xiaoning Analysis of PDEs General Relativity and Quantum Cosmology In this paper, we investigate the characteristic initial value problem for the Einstein-Dirac system, a model governing the interaction between gravity and spin-$1/2$ fields. We apply Luk's strategy \cite{Luk12} and prove a semi-global existence result for this coupled Einstein-Dirac system without imposing symmetry conditions. More precisely, we construct smooth solutions in a rectangular region to the future of two intersecting null hypersurfaces, on which characteristic initial data are specified. The key novelty is to promote the symmetric spinorial derivatives of the Dirac field to independent variables and to derive a commuted "Weyl-curvature-free" evolution system for them. This eliminates the coupling to the curvature in the energy estimates and closes the bootstrap at the optimal derivative levels. The analysis relies on a double null foliation and incorporates spinor-specific techniques essential to handling the structure of the Dirac field. |
| title | On the local existence for the characteristic initial value problem for the Einstein-Dirac system |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2509.04167 |