Perturbation theory for gravitational shadows in static spherically symmetric spacetimes

TL;DR

This paper develops a perturbation theory to analyze gravitational shadows in static spherically symmetric spacetimes, providing analytical expansions and demonstrating good accuracy even for significant deviations from standard metrics.

Contribution

The paper introduces a perturbation framework for gravitational shadows based on mass-energy ratio and metric deviations, including second-order expansions and analytical examples.

Findings

Explicit second-order expansions of shadow radius.

Reconstruction of metric expansion from shadow data.

Perturbative results remain accurate for large deviations.

Abstract

We develop a perturbation theory for surfaces confining photons and massive particles in static spherically symmetric spacetimes in terms of two parameters: the mass-to-energy ratio and the deviation of metric functions from a given form, e.g., the Schwarzschild solution. Expansions of the gravitational shadow radius in terms of these parameters are constructed up to the second order. The metric expansion in terms of the Schwarzschild mass-to-radius ratio is then reconstructed. Explicit analytical examples of non-standard black hole metrics are considered as an illustration. In some cases perturbative results demonstrate good accuracy even for non-small deviations.