Twistor initial data characterisation of pp-waves
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909163512135680 |
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| author | Gasperin, Edgar Pais, Francisco |
| author_facet | Gasperin, Edgar Pais, Francisco |
| contents | This note gives a concise derivation of a twistor-initial-data characterisation of pp-wave spacetimes in vacuum. The construction is based on a similar calculation for the Minkowski spacetime in [Class. Quantum Grav. 28 075010]. The key difference is that for the Minkowski spacetime a necessary condition is that $\nabla_{A}{}^{A'}\barκ_{A'} \neq 0$. In this note it is shown that if $\nabla_{A}{}^{A'}\barκ_{A'}=0$ then the development is a pp-wave spacetime. Furthermore, it is shown that such condition propagates off the initial hypersurface, which, in turn, gives a twistor initial data characterisation of pp-waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05883 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twistor initial data characterisation of pp-waves Gasperin, Edgar Pais, Francisco General Relativity and Quantum Cosmology This note gives a concise derivation of a twistor-initial-data characterisation of pp-wave spacetimes in vacuum. The construction is based on a similar calculation for the Minkowski spacetime in [Class. Quantum Grav. 28 075010]. The key difference is that for the Minkowski spacetime a necessary condition is that $\nabla_{A}{}^{A'}\barκ_{A'} \neq 0$. In this note it is shown that if $\nabla_{A}{}^{A'}\barκ_{A'}=0$ then the development is a pp-wave spacetime. Furthermore, it is shown that such condition propagates off the initial hypersurface, which, in turn, gives a twistor initial data characterisation of pp-waves. |
| title | Twistor initial data characterisation of pp-waves |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2404.05883 |