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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2408.11284 |
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| _version_ | 1866914947723689984 |
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| author | Saida, Hiromi Matsui, Sena A. Takeuchi, Tsutomu T. Nishiyama, Shogo Saitou, Rio Takamori, Yohsuke Takahashi, Masaaki |
| author_facet | Saida, Hiromi Matsui, Sena A. Takeuchi, Tsutomu T. Nishiyama, Shogo Saitou, Rio Takamori, Yohsuke Takahashi, Masaaki |
| contents | We have performed a parametrized post-Newtonian (PPN) test of a black hole spacetime using observational data of the star S0-2/S2 orbiting the massive black hole at our galactic center Sgr A*. After introducing our PPN model of black hole spacetime, we report the result of $χ^2$ fitting of the PPN model with the observational data. A new finding through our PPN model is a detectability of the gravitational lens effect on the null geodesics connecting S0-2 and observer under the present observational uncertainties, if a PPN parameter is about one order larger than the value for general relativity case. On the other hand, the effect of black hole spin on the S0-2's motion is not detectable. Thus our present PPN test is performed with spherically symmetric vacuum black hole spacetime. The resultant value of the PPN parameter, which corresponds to the minimum $χ^2$, implies that the gravitational field of Sgr A* is not of Schwarzschild metric or that there exists a sufficient amount of dark matters around Sgr A* to be detected by present telescopes. However, the difference between the minimum $χ^2$ and the $χ^2$ of Schwarzschild case is not large enough to ensure a statistical significance of non-Schwarzschild result. A more precise statistical analysis than $χ^2$ statistics is necessary to extract a statistically significant information of the gravitational field of Sgr A* from present observational data. We will report a result by a Bayesian analysis in next paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parametrized-Post-Newtonian Test of Black Hole Spacetime for Galactic Center Massive Black Hole Sgr A*: Formulation and $χ^2$ Fitting Saida, Hiromi Matsui, Sena A. Takeuchi, Tsutomu T. Nishiyama, Shogo Saitou, Rio Takamori, Yohsuke Takahashi, Masaaki General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory We have performed a parametrized post-Newtonian (PPN) test of a black hole spacetime using observational data of the star S0-2/S2 orbiting the massive black hole at our galactic center Sgr A*. After introducing our PPN model of black hole spacetime, we report the result of $χ^2$ fitting of the PPN model with the observational data. A new finding through our PPN model is a detectability of the gravitational lens effect on the null geodesics connecting S0-2 and observer under the present observational uncertainties, if a PPN parameter is about one order larger than the value for general relativity case. On the other hand, the effect of black hole spin on the S0-2's motion is not detectable. Thus our present PPN test is performed with spherically symmetric vacuum black hole spacetime. The resultant value of the PPN parameter, which corresponds to the minimum $χ^2$, implies that the gravitational field of Sgr A* is not of Schwarzschild metric or that there exists a sufficient amount of dark matters around Sgr A* to be detected by present telescopes. However, the difference between the minimum $χ^2$ and the $χ^2$ of Schwarzschild case is not large enough to ensure a statistical significance of non-Schwarzschild result. A more precise statistical analysis than $χ^2$ statistics is necessary to extract a statistically significant information of the gravitational field of Sgr A* from present observational data. We will report a result by a Bayesian analysis in next paper. |
| title | Parametrized-Post-Newtonian Test of Black Hole Spacetime for Galactic Center Massive Black Hole Sgr A*: Formulation and $χ^2$ Fitting |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.11284 |