Perturbation theory for gravitational shadows in static spherically symmetric spacetimes

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 nonstandard black hole metrics are considered as an illustration. In some cases perturbative results demonstrate good accuracy even for nonsmall deviations.