Self-dual gravity in de Sitter space: lightcone ansatz and static-patch scattering
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914708407189504 |
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| author | Neiman, Yasha |
| author_facet | Neiman, Yasha |
| contents | Using Krasnov's formulation of General Relativity (GR), we develop a lightcone ansatz for self-dual gravity (along with linearized anti-self-dual perturbations) in the Poincare patch of de Sitter space. This amounts to a generalization of Plebanski's "second heavenly equation" to non-zero cosmological constant. The only interaction vertices are cubic ones, found previously by Metsaev in a bottom-up lightcone approach. We point out a special feature of these vertices, which leads to "almost conservation" of energy at each successive order in perturbation theory, despite the time-dependent de Sitter background. Since we embed the lightcone variables into a full spacetime metric, the solutions have a clear geometric interpretation. In particular, this allows us to read off boundary data on both the past and future horizons of a causal (static) patch. In this way, we add self-dual GR to the program of defining & computing scattering amplitudes in a causal patch of de Sitter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17866 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-dual gravity in de Sitter space: lightcone ansatz and static-patch scattering Neiman, Yasha General Relativity and Quantum Cosmology High Energy Physics - Theory Using Krasnov's formulation of General Relativity (GR), we develop a lightcone ansatz for self-dual gravity (along with linearized anti-self-dual perturbations) in the Poincare patch of de Sitter space. This amounts to a generalization of Plebanski's "second heavenly equation" to non-zero cosmological constant. The only interaction vertices are cubic ones, found previously by Metsaev in a bottom-up lightcone approach. We point out a special feature of these vertices, which leads to "almost conservation" of energy at each successive order in perturbation theory, despite the time-dependent de Sitter background. Since we embed the lightcone variables into a full spacetime metric, the solutions have a clear geometric interpretation. In particular, this allows us to read off boundary data on both the past and future horizons of a causal (static) patch. In this way, we add self-dual GR to the program of defining & computing scattering amplitudes in a causal patch of de Sitter space. |
| title | Self-dual gravity in de Sitter space: lightcone ansatz and static-patch scattering |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2303.17866 |