Null Geodesics and Shadow Structure in Einstein–Weyl Gravity

We investigate null geodesics, photon spheres and black hole shadows for the static spherically symmetric non-Schwarzschild black hole solution of Einstein–Weyl gravity, a higher-derivative extension of General Relativity containing a quadratic Weyl-curvature term. Such higher-curvature theories are motivated by attempts to formulate a quantum theory of gravity, where they improve the ultraviolet behaviour of the gravitational interaction, and also arise naturally as effective descriptions in approaches such as string theory. We employ the numerical black hole solution obtained by Lü et al. to compute the photon sphere, the shadow radius and the angular size of the shadow as observed by static observers. We show that, for black holes of equal mass, the photon sphere, shadow radius and angular size are consistently larger than those of the corresponding Schwarzschild black hole, with the deviations increasing monotonically with the higher-curvature coupling parameter α. Motivated by the Event Horizon Telescope observations of M87* and Sagittarius A*, we further compare the predicted shadow size with current observational uncertainties and derive phenomenological upper bounds on the dimensionless coupling α/m2. These results demonstrate that black hole shadow observations provide a promising avenue for testing Einstein–Weyl gravity and constraining quantum-motivated higher-curvature corrections to General Relativity.