Instability of marginally outer trapped surfaces from initial data set symmetry
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915342603780096 |
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| author | Sherif, Abbas M. |
| author_facet | Sherif, Abbas M. |
| contents | Let $(\tildeΣ,h_{ab},K_{ab})$ be an initial data set and let $x^a$ be a symmetry vector of $\tildeΣ$. Consider a MOTS $\mathcal{S}$ in $\tildeΣ$ and let the symmetry vector be decomposable along the unit normal to $\mathcal{S}$ in $\tildeΣ$, and along $\mathcal{S}$. In this note we present some basic results with regards to the stability of $\mathcal{S}$. The vector decomposition allows us to characterize the instability of $\mathcal{S}$ by the nature of the zero set of the normal component to $\mathcal{S}$ and the divergence of the component along $\mathcal{S}$. Further observations are made under the assumption of $\mathcal{S}$ having a constant mean curvature, and $\tildeΣ$ being an Einstein manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Instability of marginally outer trapped surfaces from initial data set symmetry Sherif, Abbas M. Differential Geometry General Relativity and Quantum Cosmology Let $(\tildeΣ,h_{ab},K_{ab})$ be an initial data set and let $x^a$ be a symmetry vector of $\tildeΣ$. Consider a MOTS $\mathcal{S}$ in $\tildeΣ$ and let the symmetry vector be decomposable along the unit normal to $\mathcal{S}$ in $\tildeΣ$, and along $\mathcal{S}$. In this note we present some basic results with regards to the stability of $\mathcal{S}$. The vector decomposition allows us to characterize the instability of $\mathcal{S}$ by the nature of the zero set of the normal component to $\mathcal{S}$ and the divergence of the component along $\mathcal{S}$. Further observations are made under the assumption of $\mathcal{S}$ having a constant mean curvature, and $\tildeΣ$ being an Einstein manifold. |
| title | Instability of marginally outer trapped surfaces from initial data set symmetry |
| topic | Differential Geometry General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2502.11581 |