Construction of gravitational instantons with non-maximal volume growth via codimension-1 collapse
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916298729979904 |
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| author | Salm, Willem Adriaan |
| author_facet | Salm, Willem Adriaan |
| contents | In this paper, we construct families of gravitational instantons of type ALG, ALG*, ALH and ALH* using a gluing construction. Away from a finite set of exceptional points, the metric collapses with bounded curvature to a quotient of $\mathbb{R}^3$ by $\mathbb{Z}_2$ and a lattice of rank one or two. Depending on whether the gravitational instantons are of type ALG/ALG* or ALH/ALH*, there are either two or four exceptional points respectively that are modelled on the Atiyah-Hitchin manifold. The other exceptional points are modelled on the Taub-NUT metric. There are at most four, respectively eight, of these points in each case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of gravitational instantons with non-maximal volume growth via codimension-1 collapse Salm, Willem Adriaan Differential Geometry 53C25, 53C26, 53C55 In this paper, we construct families of gravitational instantons of type ALG, ALG*, ALH and ALH* using a gluing construction. Away from a finite set of exceptional points, the metric collapses with bounded curvature to a quotient of $\mathbb{R}^3$ by $\mathbb{Z}_2$ and a lattice of rank one or two. Depending on whether the gravitational instantons are of type ALG/ALG* or ALH/ALH*, there are either two or four exceptional points respectively that are modelled on the Atiyah-Hitchin manifold. The other exceptional points are modelled on the Taub-NUT metric. There are at most four, respectively eight, of these points in each case. |
| title | Construction of gravitational instantons with non-maximal volume growth via codimension-1 collapse |
| topic | Differential Geometry 53C25, 53C26, 53C55 |
| url | https://arxiv.org/abs/2406.16318 |