Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911204210900992 |
|---|---|
| author | Hirsch, Sven Huang, Lan-Hsuan |
| author_facet | Hirsch, Sven Huang, Lan-Hsuan |
| contents | We address two problems concerning the ADM mass-minimizing initial data sets. First, we show that the equality case of the positive mass theorem embeds into a pp-wave spacetime. Second, we show that positive Bartnik mass minimizers embed into strongly stationary vacuum spacetimes, thereby confirming the Bartnik stationary vacuum conjecture. A key ingredient is a new monotonicity formula for the Lorentzian length of a causal Killing vector field, which, among other applications, yields a strong maximum principle for the length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers Hirsch, Sven Huang, Lan-Hsuan General Relativity and Quantum Cosmology Differential Geometry We address two problems concerning the ADM mass-minimizing initial data sets. First, we show that the equality case of the positive mass theorem embeds into a pp-wave spacetime. Second, we show that positive Bartnik mass minimizers embed into strongly stationary vacuum spacetimes, thereby confirming the Bartnik stationary vacuum conjecture. A key ingredient is a new monotonicity formula for the Lorentzian length of a causal Killing vector field, which, among other applications, yields a strong maximum principle for the length. |
| title | Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2510.10306 |