Covariant Dynamical Systems Formulation of the Tolman-Oppenheimer-Volkoff Equations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910257028005888 |
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| author | Bittencourt, Eduardo Campbell, Mariam Dunsby, Peter K. S. Jorás, Sergio E. |
| author_facet | Bittencourt, Eduardo Campbell, Mariam Dunsby, Peter K. S. Jorás, Sergio E. |
| contents | We revisit static, spherically symmetric perfect-fluid stellar models in General Relativity within the framework of the $1+1+2$ semi-tetrad formalism. For locally rotationally symmetric static spacetimes, the Tolman-Oppenheimer-Volkoff system can be expressed as a covariant first-order dynamical system and, after suitable normalization, reformulated as a three-dimensional autonomous flow for a general equation of state (EoS). In the case of a linear EoS, the system reduces further to a planar dynamical system whose finite and asymptotic equilibrium points, together with their stability properties, admit a clear geometrical interpretation in terms of covariant variables. For more general equations of state, such as the polytropic case, the dynamics naturally acquire a genuinely three-dimensional character. Beyond providing a compact, covariant, and physically transparent reformulation of the relativistic stellar problem, the present analysis clarifies how the standard metric description is encoded within a global phase-space structure constructed from geometrically meaningful covariant variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26187 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Covariant Dynamical Systems Formulation of the Tolman-Oppenheimer-Volkoff Equations Bittencourt, Eduardo Campbell, Mariam Dunsby, Peter K. S. Jorás, Sergio E. General Relativity and Quantum Cosmology Mathematical Physics We revisit static, spherically symmetric perfect-fluid stellar models in General Relativity within the framework of the $1+1+2$ semi-tetrad formalism. For locally rotationally symmetric static spacetimes, the Tolman-Oppenheimer-Volkoff system can be expressed as a covariant first-order dynamical system and, after suitable normalization, reformulated as a three-dimensional autonomous flow for a general equation of state (EoS). In the case of a linear EoS, the system reduces further to a planar dynamical system whose finite and asymptotic equilibrium points, together with their stability properties, admit a clear geometrical interpretation in terms of covariant variables. For more general equations of state, such as the polytropic case, the dynamics naturally acquire a genuinely three-dimensional character. Beyond providing a compact, covariant, and physically transparent reformulation of the relativistic stellar problem, the present analysis clarifies how the standard metric description is encoded within a global phase-space structure constructed from geometrically meaningful covariant variables. |
| title | Covariant Dynamical Systems Formulation of the Tolman-Oppenheimer-Volkoff Equations |
| topic | General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2605.26187 |