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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2312.17724 |
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| _version_ | 1866916108233080832 |
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| author | Ye, Jing-Peng He, Zhi-Qing Zhou, Ai-Xu Huang, Zi-Yang Huang, Jia-Hui |
| author_facet | Ye, Jing-Peng He, Zhi-Qing Zhou, Ai-Xu Huang, Zi-Yang Huang, Jia-Hui |
| contents | Recently, a black hole model in loop quantum gravity has been proposed by Lewandowski, Ma, Yang and Zhang (Phys. Rev. Lett. \textbf{130}, 101501 (2023)). The metric tensor of the quantum black hole (QBH) is a suitably modified Schwarzschild one. In this paper, we calculate the radius of light ring and obtain the linear approximation of it with respect to the quantum correction parameter $α$: $r_{l} \simeq 3 M - \fracα{9 M}$. We then assume the QBH is backlit by a large, distant plane of uniform, isotropic emission and calculate the radius of the black hole shadow and its linear approximation: $r_{s} = 3 \sqrt{3} M - \fracα{6 \left(\sqrt{3} M\right)}$. We also consider the photon ring structures in the shadow when the impact parameter $b$ of the photon approaches to a critical impact parameter $b_{\textrm{c}}$, and obtain a formula for estimating the deflection angle, which is $φ_{\textrm{def}} = - \frac{\sqrt{2}}{ωr_{l}^2}\log{\left(b - b_c\right) + \widetilde{C}(b)}$. We also numerically plot the images of shadows and photon rings of the QBH in three different illumination models and compare them with that of a Schwarzschild in each model. It is found that we could distinguish the quantum black hole with a Schwarzschild black hole by the shadow images in certain specific illumination model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17724 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shadows and photon rings of a quantum black hole Ye, Jing-Peng He, Zhi-Qing Zhou, Ai-Xu Huang, Zi-Yang Huang, Jia-Hui General Relativity and Quantum Cosmology High Energy Physics - Theory Recently, a black hole model in loop quantum gravity has been proposed by Lewandowski, Ma, Yang and Zhang (Phys. Rev. Lett. \textbf{130}, 101501 (2023)). The metric tensor of the quantum black hole (QBH) is a suitably modified Schwarzschild one. In this paper, we calculate the radius of light ring and obtain the linear approximation of it with respect to the quantum correction parameter $α$: $r_{l} \simeq 3 M - \fracα{9 M}$. We then assume the QBH is backlit by a large, distant plane of uniform, isotropic emission and calculate the radius of the black hole shadow and its linear approximation: $r_{s} = 3 \sqrt{3} M - \fracα{6 \left(\sqrt{3} M\right)}$. We also consider the photon ring structures in the shadow when the impact parameter $b$ of the photon approaches to a critical impact parameter $b_{\textrm{c}}$, and obtain a formula for estimating the deflection angle, which is $φ_{\textrm{def}} = - \frac{\sqrt{2}}{ωr_{l}^2}\log{\left(b - b_c\right) + \widetilde{C}(b)}$. We also numerically plot the images of shadows and photon rings of the QBH in three different illumination models and compare them with that of a Schwarzschild in each model. It is found that we could distinguish the quantum black hole with a Schwarzschild black hole by the shadow images in certain specific illumination model. |
| title | Shadows and photon rings of a quantum black hole |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.17724 |