Classify horizon and geodesic configurations across the full parameter space

Classify the possible apparent-horizon and geodesic configurations of the regularized McVittie spacetime across its full parameter space, and quantify the associated violations of the standard energy conditions.

Background

The paper introduces radial and cosmological regularization scales that produce black-hole, black-bounce, and traversable-wormhole regimes within a McVittie-like cosmological setting. The apparent-horizon locations are generally determined only implicitly through higher-order polynomial equations, while the geodesic analysis is carried out primarily in a quasi-static approximation.

The authors explicitly identify a systematic analysis of the complete parameter space as unresolved. Such an analysis would need to determine how the mass, radial regularization scale, cosmological regularization scale, and expansion history jointly control horizon structure, circular and null geodesics, and the magnitude and domain of energy-condition violations.