Quantum-corrected slowly rotating wormholes: Frame dragging, photon rings, and shadows

In this study, we explore how photons move around slowly rotating wormholes, maintained by the subtle interplay of non-commutative geometry and Casimir vacuum energy. Our aim is to understand how quantum-corrected redshift profiles and rotation influence photon-sphere locations and shape the shadows an observer would see. Photon spheres—where light can orbit at a fixed radius—are highly sensitive to the wormhole’s gravitational structure. Quantum effects from non-commutative smearing and Casimir energy gently modify the gravitational potential near the throat, leading to small but meaningful shifts in the photon-sphere radius. Gaussian smearing produces mild inward shifts, nonlocal gamma-type profiles spread corrections over a broader region, and Lorentzian profiles, concentrated near the throat, generate the largest deviations. Rotation introduces frame-dragging effects, subtly pulling co-rotating photons inward while pushing counter-rotating photons outward, resulting in two closely spaced photon rings. The impact of this splitting depends on the wormhole’s angular momentum and the steepness of the quantum-corrected redshift, with Lorentzian profiles creating the most noticeable asymmetry. Consequently, the shadow’s shape reflects these effects: Gaussian profiles yield nearly circular shadows, gamma-type profiles produce moderate asymmetry, and Lorentzian profiles generate the most pronounced distortions. The quantum energy density and radial violation of the null energy condition stabilize the throat and determine photon-sphere positions. Together, quantum smearing, Casimir energy, and slow rotation encode subtle directional biases in photon paths, shaping the wormhole’s visible shadow. In essence, quantum effects set the gravitational stage, while rotation adds a delicate directional twist, together crafting the wormhole’s observable signature.