Black holes and their shadows in $F(R)$ gravity
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929637595021312 |
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| author | Nojiri, Shin'ichi Odintsov, S. D. |
| author_facet | Nojiri, Shin'ichi Odintsov, S. D. |
| contents | We investigate the radii of the photon sphere and the black hole shadow in the framework of $F(R)$ gravity. For this purpose, we derive the field equation for the corresponding theory when the general spherically symmetric and static configuration is considered. This equation is the third-order differential equation with respect to $F_R(r)\equiv \left. \frac{dF(R)}{dR}\right|_{R=R(r)}$, where $r$ is the radial coordinate. Solving the equation, we find $F(R)$ as a function of $r$, $F_R=F_R(r)$. By using the assumed and obtained geometry, one can calculate the scalar curvature $R$ as a function of $r$, $R=R(r)$, which could be solved with respect to $r$ as $r=r(R)$. Then one finds the functional form of $F_R$ as a function of the scalar curvature $R$, $F_R=F_R(R)=F_R\left( r=r\left(R\right)\right)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13775 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Black holes and their shadows in $F(R)$ gravity Nojiri, Shin'ichi Odintsov, S. D. General Relativity and Quantum Cosmology High Energy Physics - Theory We investigate the radii of the photon sphere and the black hole shadow in the framework of $F(R)$ gravity. For this purpose, we derive the field equation for the corresponding theory when the general spherically symmetric and static configuration is considered. This equation is the third-order differential equation with respect to $F_R(r)\equiv \left. \frac{dF(R)}{dR}\right|_{R=R(r)}$, where $r$ is the radial coordinate. Solving the equation, we find $F(R)$ as a function of $r$, $F_R=F_R(r)$. By using the assumed and obtained geometry, one can calculate the scalar curvature $R$ as a function of $r$, $R=R(r)$, which could be solved with respect to $r$ as $r=r(R)$. Then one finds the functional form of $F_R$ as a function of the scalar curvature $R$, $F_R=F_R(R)=F_R\left( r=r\left(R\right)\right)$. |
| title | Black holes and their shadows in $F(R)$ gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.13775 |