Relativistic Virial Theorem, Limiting Compactness, and the end state of gravitational collapse
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915286994649088 |
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| author | Dadhich, Naresh |
| author_facet | Dadhich, Naresh |
| contents | It is noteworthy that limiting compactness of a static bounded configuration is characterized by a general principle: \textit{one, by equipartition of mass between inside and outside, and the other by vanishing of energy inside.} The former implies gravitational energy being half of mass leading to limiting compactness $M/R = 4/9$ of Buchdahl star while for the latter, the two are equal giving $M/R = 1/2$ of black hole with horizon. \emph{This is the relativistic Virial theorem respectively for massive and massless particles.} It is remarkable that it prescribes that there can exist only two equilibrium states which also define limiting compactness of the object. Consequently, it leads to a profound prediction that the ultimate endproduct of gravitational collapse could only be one of the two, Buchdahl star or black hole. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relativistic Virial Theorem, Limiting Compactness, and the end state of gravitational collapse Dadhich, Naresh General Relativity and Quantum Cosmology It is noteworthy that limiting compactness of a static bounded configuration is characterized by a general principle: \textit{one, by equipartition of mass between inside and outside, and the other by vanishing of energy inside.} The former implies gravitational energy being half of mass leading to limiting compactness $M/R = 4/9$ of Buchdahl star while for the latter, the two are equal giving $M/R = 1/2$ of black hole with horizon. \emph{This is the relativistic Virial theorem respectively for massive and massless particles.} It is remarkable that it prescribes that there can exist only two equilibrium states which also define limiting compactness of the object. Consequently, it leads to a profound prediction that the ultimate endproduct of gravitational collapse could only be one of the two, Buchdahl star or black hole. |
| title | Relativistic Virial Theorem, Limiting Compactness, and the end state of gravitational collapse |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2504.00064 |