Solutions to the Ricci Flow via Einstein Field Equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915022107574272 |
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| author | Morone, Tommaso Tateo, Roberto |
| author_facet | Morone, Tommaso Tateo, Roberto |
| contents | We show how solutions to the Ricci flow on Lorentzian manifolds, along with its generalizations, can be linked to Einstein's field equations. The approach involves deformations of the matter sector that are generated by quadratic functionals of the stress-energy tensor. We provide illustrative examples by explicitly constructing analytical solutions within maximally symmetric spacetimes and in the context of Born-Infeld's nonlinear electrodynamics. Finally, we discuss configurations involving global topological monopoles, emphasizing the versatility of this approach across various geometric and physical settings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions to the Ricci Flow via Einstein Field Equations Morone, Tommaso Tateo, Roberto High Energy Physics - Theory We show how solutions to the Ricci flow on Lorentzian manifolds, along with its generalizations, can be linked to Einstein's field equations. The approach involves deformations of the matter sector that are generated by quadratic functionals of the stress-energy tensor. We provide illustrative examples by explicitly constructing analytical solutions within maximally symmetric spacetimes and in the context of Born-Infeld's nonlinear electrodynamics. Finally, we discuss configurations involving global topological monopoles, emphasizing the versatility of this approach across various geometric and physical settings. |
| title | Solutions to the Ricci Flow via Einstein Field Equations |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.10265 |