Single-rotating Five-dimensional Near-horizon Extremal Geometry in General Relativity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929249732001792 |
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| author | Hajian, Kamal |
| author_facet | Hajian, Kamal |
| contents | The geometries with SL$(2,\mathbb{R})$ and some axial U$(1)$ isometries are called ``near-horizon extremal geometries" and are found usually, but not necessarily, in the near-horizon limit of the extremal black holes. We present a new member of this family of solutions in five-dimensional Einstein-Hilbert gravity that has only one nonzero angular momentum. In contrast with the single-rotating Myers-Perry extremal black hole and its near-horizon geometry in five dimensions, this solution may have a nonvanishing and finite entropy. Although there is a uniqueness theorem that prohibits the existence of such single-rotating near-horizon geometries in five-dimensional general relativity, this solution has a curvature singularity at one of the poles, which breaks the smoothness conditions in the theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_16534 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Single-rotating Five-dimensional Near-horizon Extremal Geometry in General Relativity Hajian, Kamal General Relativity and Quantum Cosmology High Energy Physics - Theory The geometries with SL$(2,\mathbb{R})$ and some axial U$(1)$ isometries are called ``near-horizon extremal geometries" and are found usually, but not necessarily, in the near-horizon limit of the extremal black holes. We present a new member of this family of solutions in five-dimensional Einstein-Hilbert gravity that has only one nonzero angular momentum. In contrast with the single-rotating Myers-Perry extremal black hole and its near-horizon geometry in five dimensions, this solution may have a nonvanishing and finite entropy. Although there is a uniqueness theorem that prohibits the existence of such single-rotating near-horizon geometries in five-dimensional general relativity, this solution has a curvature singularity at one of the poles, which breaks the smoothness conditions in the theorem. |
| title | Single-rotating Five-dimensional Near-horizon Extremal Geometry in General Relativity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2307.16534 |