Perturbation theory for gravitational shadows in Kerr-like spacetimes

TL;DR

This paper introduces an analytical perturbation method to compute key parameters of Kerr-like gravitational shadows, accurately accounting for plasma effects, reducing reliance on numerical integration.

Contribution

The paper develops a perturbation theory-based analytical framework to calculate gravitational shadow parameters for Kerr-like spacetimes, including plasma effects, with high accuracy.

Findings

Derived polynomial expressions for shadow parameters with ~a^5 accuracy.

Eliminated the need for repeated numerical integration.

Accounted for plasma effects in shadow calculations.

Abstract

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 $\delta C$, 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 multi-frequency astrophysical observations.