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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2412.17520 |
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| _version_ | 1866912167378288640 |
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| author | Li, Shi-Yu Luo, Song-Shan Feng, Zhong-Wen |
| author_facet | Li, Shi-Yu Luo, Song-Shan Feng, Zhong-Wen |
| contents | This study investigates photon orbits around Kerr-MOG black holes. The equation of photon of motion around the Kerr-MOG black hole is derived by solving the Hamilton-Jacobi equation, expressed as a sixth-order polynomial involving the inclination angle $v$, the rotation parameter $u$, and the deformation parameter $α$ that characterizes modified gravity. We find that $α$ constrains the rotation of the black hole, modifying its gravitational field and leading to distinct photon orbital characteristics. Numerical analysis reveals that the polar plane ($v=1$) has two effective orbits: one outside and one inside the event horizon, while the equatorial plane ($v=0$) has four effective orbits: two outside and two inside the event horizon. Moreover, we derive the exact formula for general photon orbits between the polar and equatorial planes ($0<v<1$). In the extremal case, the rotation speed significantly impacts general photon orbits. A slowly rotating extremal black hole has two general photon orbits outside the event horizon, whereas a rapidly rotating extremal black hole has only one such orbit. In the non-extremal case, a critical inclination angle $v_{cr}$ exists in the parameter space $\left(v, u, α\right)$. Below $v_{cr}$, there are four general photon orbits, while above $v_{cr}$, there are two orbits. At the critical inclination angle, three solutions are found: two photon orbits outside and one inside the event horizon. Additionally, the results indicate that all orbits are radially unstable. Furthermore, by analyzing photon impact parameter, we argue that $α$ influences observational properties of the black hole. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17520 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spherical photon orbits around Kerr-MOG black hole Li, Shi-Yu Luo, Song-Shan Feng, Zhong-Wen General Relativity and Quantum Cosmology This study investigates photon orbits around Kerr-MOG black holes. The equation of photon of motion around the Kerr-MOG black hole is derived by solving the Hamilton-Jacobi equation, expressed as a sixth-order polynomial involving the inclination angle $v$, the rotation parameter $u$, and the deformation parameter $α$ that characterizes modified gravity. We find that $α$ constrains the rotation of the black hole, modifying its gravitational field and leading to distinct photon orbital characteristics. Numerical analysis reveals that the polar plane ($v=1$) has two effective orbits: one outside and one inside the event horizon, while the equatorial plane ($v=0$) has four effective orbits: two outside and two inside the event horizon. Moreover, we derive the exact formula for general photon orbits between the polar and equatorial planes ($0<v<1$). In the extremal case, the rotation speed significantly impacts general photon orbits. A slowly rotating extremal black hole has two general photon orbits outside the event horizon, whereas a rapidly rotating extremal black hole has only one such orbit. In the non-extremal case, a critical inclination angle $v_{cr}$ exists in the parameter space $\left(v, u, α\right)$. Below $v_{cr}$, there are four general photon orbits, while above $v_{cr}$, there are two orbits. At the critical inclination angle, three solutions are found: two photon orbits outside and one inside the event horizon. Additionally, the results indicate that all orbits are radially unstable. Furthermore, by analyzing photon impact parameter, we argue that $α$ influences observational properties of the black hole. |
| title | Spherical photon orbits around Kerr-MOG black hole |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.17520 |