Introducing Various Notions of Distances between Space-Times
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915555218292736 |
|---|---|
| author | Sakovich, Anna Sormani, Christina |
| author_facet | Sakovich, Anna Sormani, Christina |
| contents | We introduce the notion of causally-null-compactifiable space-times which can be canonically converted into a compact timed-metric-spaces using the cosmological time of Andersson-Howard-Galloway and the null distance of Sormani-Vega. We produce a large class of such space-times including future developments of compact initial data sets and regions which exhaust asymptotically flat space-times. We then present various notions of intrinsic distances between these space-times (introducing the timed-Hausdorff distance) and prove some of these notions of distance are definite in the sense that they equal zero iff there is a time-oriented Lorentzian isometry between the space-times. These definite distances enable us to define various notions of convergence of space-times to limit space-times which are not necessarily smooth. Many open questions and conjectures are included throughout. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16800 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Introducing Various Notions of Distances between Space-Times Sakovich, Anna Sormani, Christina Differential Geometry General Relativity and Quantum Cosmology 83C99, 58Z05, 30L05 We introduce the notion of causally-null-compactifiable space-times which can be canonically converted into a compact timed-metric-spaces using the cosmological time of Andersson-Howard-Galloway and the null distance of Sormani-Vega. We produce a large class of such space-times including future developments of compact initial data sets and regions which exhaust asymptotically flat space-times. We then present various notions of intrinsic distances between these space-times (introducing the timed-Hausdorff distance) and prove some of these notions of distance are definite in the sense that they equal zero iff there is a time-oriented Lorentzian isometry between the space-times. These definite distances enable us to define various notions of convergence of space-times to limit space-times which are not necessarily smooth. Many open questions and conjectures are included throughout. |
| title | Introducing Various Notions of Distances between Space-Times |
| topic | Differential Geometry General Relativity and Quantum Cosmology 83C99, 58Z05, 30L05 |
| url | https://arxiv.org/abs/2410.16800 |