Gravitational Black Hole Shadow Spectroscopy

TL;DR

The paper advances black-hole shadow diagnostics by formulating a fully generalized perturbative framework for massive-particle shadows in static, spherically symmetric spacetimes, allowing simultaneous perturbations of all metric functions and relaxing the fixed area gauge $\beta(r)=r^2$. By expanding both the metric and the particle energy-dependence to second order, it derives explicit expressions for the first- and second-order corrections to the massive shadow radius $R^2(\epsilon,\delta)$, revealing nonlinear couplings between temporal and spatial perturbations. This shadow spectroscopy breaks degeneracies inherent in the photon shadow and enables metric reconstruction from multi-energy observations, demonstrated on the Simpson-Visser wormhole and the Fisher–Janis–Newman–Winicour scalar-tensor solution. The framework offers a practical, theory-agnostic tool for testing strong-field gravity and interpreting future high-precision, multi-messenger observations of compact objects.

Abstract

In this work, we develop a generalized perturbative framework for gravitational shadows in static, spherically symmetric spacetimes. Building upon the recent two-parameter perturbative framework of Kobialko et al. \cite{Kobialko:2024zhc}, this work extends the expansion in particle energy and metric deviation to encompass arbitrary, simultaneous deformations of all metric functions. By relaxing the common restriction of a fixed area radius $(β(r) = r^2)$, our formalism applies to a significantly broader class of alternative gravity theories and exotic compact objects. We derive analytical formulae for the massive shadow radius up to the second order in the deformation parameter, explicitly revealing the phenomenological signatures that arise from the coupling between temporal and spatial metric perturbations. The key result is that the distinct energy dependence of the massive shadow provides a powerful method to disentangle these different types of geometric deformations, breaking observational degeneracies inherent in the photon shadow alone. We demonstrate this principle with applications to traversable wormholes and canonical scalar-tensor solutions, showing how each produces a unique, distinguishable energy-dependent fingerprint. This generalized framework provides a robust, theory-agnostic tool for testing strong-field gravity. It offers a clear methodology for reconstructing metric parameters from potential multi-messenger observations of massive particle shadows.