Min-max minimal surfaces, horizons and electrostatic systems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866908326775750656 |
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| author | Cruz, Tiarlos Lima, Vanderson de Sousa, Alexandre |
| author_facet | Cruz, Tiarlos Lima, Vanderson de Sousa, Alexandre |
| contents | We present a connection between minimal surfaces of index one and General Relativity. First, we show that for a certain class of (electro)static systems, each of its unstable horizons is the solution of a one-parameter min-max problem for the area functional, in particular it has index one. We also obtain an inequality relating the area and the charge of a minimal surface of index one in a Cauchy data satisfying the Dominant Energy Condition for non-electromagnetic matter fields. Moreover, we explore a global version of this inequality, and the rigidity in the case of the equality, using a result proved by Marques and Neves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_08600 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Min-max minimal surfaces, horizons and electrostatic systems Cruz, Tiarlos Lima, Vanderson de Sousa, Alexandre Differential Geometry General Relativity and Quantum Cosmology We present a connection between minimal surfaces of index one and General Relativity. First, we show that for a certain class of (electro)static systems, each of its unstable horizons is the solution of a one-parameter min-max problem for the area functional, in particular it has index one. We also obtain an inequality relating the area and the charge of a minimal surface of index one in a Cauchy data satisfying the Dominant Energy Condition for non-electromagnetic matter fields. Moreover, we explore a global version of this inequality, and the rigidity in the case of the equality, using a result proved by Marques and Neves. |
| title | Min-max minimal surfaces, horizons and electrostatic systems |
| topic | Differential Geometry General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/1912.08600 |