Some inequalities among curvature invariants
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918396525805568 |
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| author | Szybka, Sebastian J. Kravetska, Yaroslava Nikiel, Kornelia |
| author_facet | Szybka, Sebastian J. Kravetska, Yaroslava Nikiel, Kornelia |
| contents | We prove an infinite sequence of inequalities among scalar polynomial invariants of symmetric rank-2 tensors of Segre types $A1$, $A3$, and $B$. In particular, these inequalities apply to the Ricci tensor and the energy-momentum tensor. If at least one of them is violated by the Ricci tensor, then the Einstein equations force violation of all classical energy conditions. In addition, we use one of the inequalities to generalize the known relation between the second Ricci invariant and the Kretschmann scalar. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_22187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some inequalities among curvature invariants Szybka, Sebastian J. Kravetska, Yaroslava Nikiel, Kornelia General Relativity and Quantum Cosmology 83C20 We prove an infinite sequence of inequalities among scalar polynomial invariants of symmetric rank-2 tensors of Segre types $A1$, $A3$, and $B$. In particular, these inequalities apply to the Ricci tensor and the energy-momentum tensor. If at least one of them is violated by the Ricci tensor, then the Einstein equations force violation of all classical energy conditions. In addition, we use one of the inequalities to generalize the known relation between the second Ricci invariant and the Kretschmann scalar. |
| title | Some inequalities among curvature invariants |
| topic | General Relativity and Quantum Cosmology 83C20 |
| url | https://arxiv.org/abs/2509.22187 |