On the Universal Cuspy Behavior in Black Hole Shadows

This work investigates the universality of cusp formation in the shadows of compact objects. The emergence of cusps is accompanied by three interrelated phenomena: a topological charge transition, an equal-area law governing the self-intersecting structure, and universal critical scaling behavior. We demonstrate that, because these phenomena originate from the global morphology of the shadow, they are fundamentally independent of specific spacetime metric details and apply across diverse models. These features are systematically analyzed for the Kerr black hole endowed with a running Newton coupling. By extending our framework to rotating traversable wormholes, we confirm that the same universal behavior persists in more general compact objects. Our study uncovers the universality underlying cusp formation, offering a model-independent framework for characterizing possible non-Kerr shadow morphologies.