A test of the conjectured critical black-hole formation -- null geodesic correspondence: The case of self-gravitating scalar fields
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914947799187456 |
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| author | Hod, Shahar |
| author_facet | Hod, Shahar |
| contents | It has recently been conjectured [A. Ianniccari {\it et al.}, Phys. Rev. Lett. {\bf 133}, 081401 (2024)] that there exists a correspondence between the critical threshold of black-hole formation and the stability properties of null circular geodesics in the curved spacetime of the collapsing matter configuration. In the present compact paper we provide a non-trivial test of this intriguing conjecture. In particular, using analytical techniques we study the physical and mathematical properties of self-gravitating scalar field configurations that possess marginally-stable (degenerate) null circular geodesics. We reveal the interesting fact that the {\it analytically} calculated critical compactness parameter ${\cal C}^{\text{analytical}}\equiv{\text{max}_r}\{m(r)/r\}=6/25$, which signals the appearance of the first (marginally-stable) null circular geodesic in the curved spacetime of the self-gravitating scalar fields, agrees quite well (to within $\sim10\%$) with the exact compactness parameter ${\cal C}^{\text{numerical}}\equiv\text{max}_t\{\text{max}_r\{m(r)/r\}\}\simeq0.265$ which is computed {\it numerically} using fully non-linear numerical simulations of the gravitational collapse of scalar fields at the threshold of black-hole formation [here $m(r)$ is the gravitational mass contained within a sphere of radius $r$]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_07517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A test of the conjectured critical black-hole formation -- null geodesic correspondence: The case of self-gravitating scalar fields Hod, Shahar General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory It has recently been conjectured [A. Ianniccari {\it et al.}, Phys. Rev. Lett. {\bf 133}, 081401 (2024)] that there exists a correspondence between the critical threshold of black-hole formation and the stability properties of null circular geodesics in the curved spacetime of the collapsing matter configuration. In the present compact paper we provide a non-trivial test of this intriguing conjecture. In particular, using analytical techniques we study the physical and mathematical properties of self-gravitating scalar field configurations that possess marginally-stable (degenerate) null circular geodesics. We reveal the interesting fact that the {\it analytically} calculated critical compactness parameter ${\cal C}^{\text{analytical}}\equiv{\text{max}_r}\{m(r)/r\}=6/25$, which signals the appearance of the first (marginally-stable) null circular geodesic in the curved spacetime of the self-gravitating scalar fields, agrees quite well (to within $\sim10\%$) with the exact compactness parameter ${\cal C}^{\text{numerical}}\equiv\text{max}_t\{\text{max}_r\{m(r)/r\}\}\simeq0.265$ which is computed {\it numerically} using fully non-linear numerical simulations of the gravitational collapse of scalar fields at the threshold of black-hole formation [here $m(r)$ is the gravitational mass contained within a sphere of radius $r$]. |
| title | A test of the conjectured critical black-hole formation -- null geodesic correspondence: The case of self-gravitating scalar fields |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.07517 |