Near horizon limit of the Wang--Yau quasi-local mass
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910557592879104 |
|---|---|
| author | Chen, Po-Ning |
| author_facet | Chen, Po-Ning |
| contents | In this article, we compute the limit of the Wang--Yau quasi-local mass on a family of surfaces approaching the apparent horizon (the near horizon limit). Such limit is first considered in [1]. Recently, Pook-Kolb, Zhao, Andersson, Krishnan, and Yau investigated the near horizon limit of the Wang--Yau quasi-local mass in binary black hole mergers in [12] and conjectured that the optimal embeddings approach the isometric embedding of the horizon into $\R^3$. Moreover, the quasi-local mass converges to the total mean curvature of the image. The vanishing of the norm of the mean curvature vector implies special properties for the Wang--Yau quasi-local energy and the optimal embedding equation. We utilize these features to prove the existence and uniqueness of the optimal embedding and investigate the minimization of the Wang--Yau quasi-local energy. In particular, we prove the continuity of the quasi-local mass in the near horizon limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Near horizon limit of the Wang--Yau quasi-local mass Chen, Po-Ning General Relativity and Quantum Cosmology Differential Geometry In this article, we compute the limit of the Wang--Yau quasi-local mass on a family of surfaces approaching the apparent horizon (the near horizon limit). Such limit is first considered in [1]. Recently, Pook-Kolb, Zhao, Andersson, Krishnan, and Yau investigated the near horizon limit of the Wang--Yau quasi-local mass in binary black hole mergers in [12] and conjectured that the optimal embeddings approach the isometric embedding of the horizon into $\R^3$. Moreover, the quasi-local mass converges to the total mean curvature of the image. The vanishing of the norm of the mean curvature vector implies special properties for the Wang--Yau quasi-local energy and the optimal embedding equation. We utilize these features to prove the existence and uniqueness of the optimal embedding and investigate the minimization of the Wang--Yau quasi-local energy. In particular, we prove the continuity of the quasi-local mass in the near horizon limit. |
| title | Near horizon limit of the Wang--Yau quasi-local mass |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2408.02917 |