Redshift Spectroscopy as a Probe of Regular Black Holes, Black Bounces, and Scalar-Hair Compact Objects

Abstract

Motivated by [Phys. Rev. D. 107, 064019 (2023)], we develop a unified and model-independent framework for the spectroscopy of photon frequency shifts in generic static, spherically symmetric spacetimes. Working with a line element characterized by three arbitrary radial metric functions, we derive exact expressions for the conserved quantities of massive and massless probes, the conditions for circular timelike geodesics, the local-emission-angle-dependent photon impact parameter, and the corresponding local redshift and blueshift branches measured by distant static observers. The formalism is further extended to include the line-of-sight peculiar motion of the source and the local propagation of photons in a nonmagnetized cold plasma, thereby identifying the gravitational, orbital, and dispersive factors entering the frequency-shift signal under the stated assumptions. We also show that, in vacuum, the same geometric structures governing orbital spectroscopy determine the photon sphere and the shadow impact parameter whenever an external null critical orbit is present. To make the framework suitable for deformed compact-object models, we construct a perturbative expansion around Schwarzschild geometry up to second order in a dimensionless deformation parameter, obtaining explicit corrections to the orbital energy, angular momentum, emitter four-velocity, photon impact parameter, and the vacuum and plasma frequency shifts. We apply the formalism to regular black holes from nonlinear electrodynamics, the Simpson--Visser black-bounce spacetime, and the Fisher--Janis--Newman--Winicour--Wyman geometry. These examples show that the same local spectroscopic language can be used across regular-black-hole, black-bounce, wormhole, and scalar-supported horizonless sectors.