One-Dimensional Relativistic Self-Gravitating Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915233871691776 |
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| author | Mann, Robert B. |
| author_facet | Mann, Robert B. |
| contents | One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here, I review what is known about the relativistic gravitational $N$-body problem. Reduction to one spatial dimension has the feature of the absence of gravitational radiation, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to $N$ point particles, I discuss in turn the two-body, three-body, four-body, and $N$-body problems. Quite general exact solutions can be obtained for the two-body problem, unlike the situation in general relativity in three spatial dimensions for which only highly specified solutions exist. The three-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For $N\geq 4$, other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06515 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-Dimensional Relativistic Self-Gravitating Systems Mann, Robert B. General Relativity and Quantum Cosmology Astrophysics of Galaxies Statistical Mechanics Mathematical Physics One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here, I review what is known about the relativistic gravitational $N$-body problem. Reduction to one spatial dimension has the feature of the absence of gravitational radiation, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to $N$ point particles, I discuss in turn the two-body, three-body, four-body, and $N$-body problems. Quite general exact solutions can be obtained for the two-body problem, unlike the situation in general relativity in three spatial dimensions for which only highly specified solutions exist. The three-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For $N\geq 4$, other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems. |
| title | One-Dimensional Relativistic Self-Gravitating Systems |
| topic | General Relativity and Quantum Cosmology Astrophysics of Galaxies Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2504.06515 |