Salm, Willem Adriaan;
(2023)
Construction of gravitational instantons with non-maximal volume growth.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
In this thesis, we construct families of gravitational instantons of type ALG, ALG*, ALH and ALH*. Away from a finite set of exceptional points, the metric collapses with bounded curvature to a quotient of R^3 by a lattice of rank one or two and Z_2. Depending on whether the gravitational instantons are of type ALG/ALG* or ALH/ALH*, there are 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. These gravitational instantons are constructed using a gluing construction, where we combine these ALF gravitational instantons to a bulk space that is constructed using the Gibbons-Hawking ansatz. We then set up a deformation argument, where we perturb these approximate solutions into genuine gravitational instantons.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Construction of gravitational instantons with non-maximal volume growth |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2023. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10171342 |
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