Weighing the curvature invariants
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915417943965696 |
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| author | Dragašević, Jan Moslavac, Ina Smolić, Ivica |
| author_facet | Dragašević, Jan Moslavac, Ina Smolić, Ivica |
| contents | We prove several inequalities between the curvature invariants, which impose constraints on curvature singularities. Some of the inequalities hold for a family of spacetimes which include static, Friedmann--Lemaître--Robertson--Walker, and Bianchi type I metrics, independently of whether they are solutions of some particular field equations. In contrast, others hold for solutions of Einstein's gravitational field equation and a family of energy-momentum tensors (featuring ideal fluids, scalar fields and nonlinear electromagnetic fields), independently of the specific form of the spacetime metric. We illustrate different behaviour of the basic curvature invariants with numerous examples and discuss the consequences and limitations of the proven results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighing the curvature invariants Dragašević, Jan Moslavac, Ina Smolić, Ivica General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We prove several inequalities between the curvature invariants, which impose constraints on curvature singularities. Some of the inequalities hold for a family of spacetimes which include static, Friedmann--Lemaître--Robertson--Walker, and Bianchi type I metrics, independently of whether they are solutions of some particular field equations. In contrast, others hold for solutions of Einstein's gravitational field equation and a family of energy-momentum tensors (featuring ideal fluids, scalar fields and nonlinear electromagnetic fields), independently of the specific form of the spacetime metric. We illustrate different behaviour of the basic curvature invariants with numerous examples and discuss the consequences and limitations of the proven results. |
| title | Weighing the curvature invariants |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2502.12242 |