Oscillatory spacelike singularities: The Bianchi type $\mathrm{VI}_{-1/9}$ vacuum models
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912558114406400 |
|---|---|
| author | Lappicy, Phillipo Uggla, Claes |
| author_facet | Lappicy, Phillipo Uggla, Claes |
| contents | The Bianchi type $\mathrm{VI}_{-1/9}$, $\mathrm{VIII}$ and $\mathrm{IX}$ vacuum models all have 4-dimensional Hubble-normalized state spaces and are expected to have a generic initial oscillatory singularity, but the invariant boundary sets responsible for the oscillations are much more complicated for type $\mathrm{VI}_{-1/9}$ than those of type $\mathrm{VIII}$ and $\mathrm{IX}$. For the first time, we explicitly solve the equations on these type $\mathrm{VI}_{-1/9}$ boundary sets and also introduce a new graph representation of the associated network of heteroclinic chains (i.e. sequences of solutions describing the oscillations). In particular, we give examples of networks of entangled cyclic heteroclinic chains and show that only some of these cyclic heteroclinic chains are asymptotically relevant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Oscillatory spacelike singularities: The Bianchi type $\mathrm{VI}_{-1/9}$ vacuum models Lappicy, Phillipo Uggla, Claes General Relativity and Quantum Cosmology Mathematical Physics Dynamical Systems The Bianchi type $\mathrm{VI}_{-1/9}$, $\mathrm{VIII}$ and $\mathrm{IX}$ vacuum models all have 4-dimensional Hubble-normalized state spaces and are expected to have a generic initial oscillatory singularity, but the invariant boundary sets responsible for the oscillations are much more complicated for type $\mathrm{VI}_{-1/9}$ than those of type $\mathrm{VIII}$ and $\mathrm{IX}$. For the first time, we explicitly solve the equations on these type $\mathrm{VI}_{-1/9}$ boundary sets and also introduce a new graph representation of the associated network of heteroclinic chains (i.e. sequences of solutions describing the oscillations). In particular, we give examples of networks of entangled cyclic heteroclinic chains and show that only some of these cyclic heteroclinic chains are asymptotically relevant. |
| title | Oscillatory spacelike singularities: The Bianchi type $\mathrm{VI}_{-1/9}$ vacuum models |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2410.10375 |