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 $\overline{R}$, the deviation from sphericity $\delta C$, and the mean deviation from the Kerr shadow $\delta K$. 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 multifrequency astrophysical observations.

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• Alternative gravity theories
• Classical black holes
• Gravitation
• Gravitational lenses