Static Stellar Phase Transitions in General Relativity and a Generalized Buchdahl Limit
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914162983043072 |
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| author | Reintjes, Moritz Xia, Ruochen |
| author_facet | Reintjes, Moritz Xia, Ruochen |
| contents | We give the first general construction of solutions of the static spherically symmetric Einstein-Euler equations, the Tolman-Oppenheimer-Volkoff (TOV-)equation, with prescribed density functions allowed to be discontinuous and non-uniform; these solutions describe stellar phase transitions in General Relativity. Boundedness of the resulting pressure functions solving the TOV-equations, from the boundary down to the stellar center, is obtained by identifying a novel condition on the prescribed density, in generalization of the classical Buchdahl limit. Moreover, we introduce a new necessary condition for the existence of such bounded pressure functions, which in the special case of a uniform density state reduces to the classical Buchdahl limit on the stellar mass-radius relationship. We present various examples to study the stellar mass-radius relationships resulting from our new conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Static Stellar Phase Transitions in General Relativity and a Generalized Buchdahl Limit Reintjes, Moritz Xia, Ruochen General Relativity and Quantum Cosmology 83C20 We give the first general construction of solutions of the static spherically symmetric Einstein-Euler equations, the Tolman-Oppenheimer-Volkoff (TOV-)equation, with prescribed density functions allowed to be discontinuous and non-uniform; these solutions describe stellar phase transitions in General Relativity. Boundedness of the resulting pressure functions solving the TOV-equations, from the boundary down to the stellar center, is obtained by identifying a novel condition on the prescribed density, in generalization of the classical Buchdahl limit. Moreover, we introduce a new necessary condition for the existence of such bounded pressure functions, which in the special case of a uniform density state reduces to the classical Buchdahl limit on the stellar mass-radius relationship. We present various examples to study the stellar mass-radius relationships resulting from our new conditions. |
| title | Static Stellar Phase Transitions in General Relativity and a Generalized Buchdahl Limit |
| topic | General Relativity and Quantum Cosmology 83C20 |
| url | https://arxiv.org/abs/2511.14287 |