Perturbation theory for gravitational shadows in Kerr-like spacetimes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918291015991296 |
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| author | Kobialko, Kirill Gal'tsov, Dmitri |
| author_facet | Kobialko, Kirill Gal'tsov, Dmitri |
| contents | We present a fully analytical method for calculating the key parameters of a Kerr-like gravitational shadow, including its horizontal and vertical diameters, $D_X$ and $D_Y$, the coordinates of its center $X_{C}$, the average radius $\bar{R}$, the deviation from sphericity $δC$, and the mean deviation from the Kerr shadow $δK$. Developed within the framework of perturbation theory, this approach yields all characteristic parameters as simple polynomial expressions with an accuracy of $\sim a^5$, where $a$ is the Kerr spin parameter. This eliminates the need for repeated numerical integration of cumbersome parametric equations. Furthermore, our derived formulas account for the effects of a plasma medium - a feature of particular relevance given the prospect of multi-frequency astrophysical observations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_24126 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perturbation theory for gravitational shadows in Kerr-like spacetimes Kobialko, Kirill Gal'tsov, Dmitri General Relativity and Quantum Cosmology We present a fully analytical method for calculating the key parameters of a Kerr-like gravitational shadow, including its horizontal and vertical diameters, $D_X$ and $D_Y$, the coordinates of its center $X_{C}$, the average radius $\bar{R}$, the deviation from sphericity $δC$, and the mean deviation from the Kerr shadow $δK$. Developed within the framework of perturbation theory, this approach yields all characteristic parameters as simple polynomial expressions with an accuracy of $\sim a^5$, where $a$ is the Kerr spin parameter. This eliminates the need for repeated numerical integration of cumbersome parametric equations. Furthermore, our derived formulas account for the effects of a plasma medium - a feature of particular relevance given the prospect of multi-frequency astrophysical observations. |
| title | Perturbation theory for gravitational shadows in Kerr-like spacetimes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2512.24126 |