Null fluid gravitational fields on Kerr manifolds and optical lifts of Sasaki structures
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| Format: | Preprint |
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2025
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| _version_ | 1866911268775919616 |
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| author | Ganji, Masoud Giannotti, Cristina Spiro, Andrea |
| author_facet | Ganji, Masoud Giannotti, Cristina Spiro, Andrea |
| contents | Building on the characterisation in [C. D. Hill, J. Lewandowski and P. Nurowski, Indiana Univ. Math. J. 57 (2008), 3131--3176] of 4-dimensional Lorentzian metrics adapted to an optical structure and satisfying the null fluid Einstein equations, we give an explicit parameterisation of this class under the assumption that the optical structure is of Kerr type. As immediate consequences, we obtain: (1) a new method for constructing solutions to the Einstein equations with a null fluid energy momentum tensor, yielding a large family of explicit metrics that naturally includes the classical Kerr black hole metrics and all Ricci flat examples described in [M. Ganji, C. Giannotti, G. Schmalz and A. Spiro, Ann. Physics 75 (2025), Paper No. 169908, 28]; (2) a solution to a conjecture in Hill, Lewandowski and Nurowski's paper on the local existence of smooth optical lifts in the case of Sasaki CR structures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_12775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Null fluid gravitational fields on Kerr manifolds and optical lifts of Sasaki structures Ganji, Masoud Giannotti, Cristina Spiro, Andrea General Relativity and Quantum Cosmology Differential Geometry 53B30, 83C05, 83C15 Building on the characterisation in [C. D. Hill, J. Lewandowski and P. Nurowski, Indiana Univ. Math. J. 57 (2008), 3131--3176] of 4-dimensional Lorentzian metrics adapted to an optical structure and satisfying the null fluid Einstein equations, we give an explicit parameterisation of this class under the assumption that the optical structure is of Kerr type. As immediate consequences, we obtain: (1) a new method for constructing solutions to the Einstein equations with a null fluid energy momentum tensor, yielding a large family of explicit metrics that naturally includes the classical Kerr black hole metrics and all Ricci flat examples described in [M. Ganji, C. Giannotti, G. Schmalz and A. Spiro, Ann. Physics 75 (2025), Paper No. 169908, 28]; (2) a solution to a conjecture in Hill, Lewandowski and Nurowski's paper on the local existence of smooth optical lifts in the case of Sasaki CR structures. |
| title | Null fluid gravitational fields on Kerr manifolds and optical lifts of Sasaki structures |
| topic | General Relativity and Quantum Cosmology Differential Geometry 53B30, 83C05, 83C15 |
| url | https://arxiv.org/abs/2511.12775 |