Rotating wormholes from quantum non-commutative geometry versus Kerr black holes: photon rings, shadows, and exotic matter localization

We construct rotating traversable wormholes supported by non-commutative matter distributions characterized by a smearing scale l . Using Gaussian and Lorentzian profiles, the shape functions remain finite everywhere and satisfy the flare-out condition with b ′( r 0 ) between 0.4 and 0.8 for throat radii r 0 in the range 1.5 to 2.5 (in geometric units). The slow-rotation approximation is employed with angular momentum values J = 0.05 , 0.15 , 0.25 , 0.35 , 0.50 and spin parameter χ = J / M 2 ≲ 0.15 . The Lense-Thirring precession frequency at the throat is Ω L T ( r 0 ) = 3 J / r 0 4 , giving dimensionless values Ω ˜ L T ≈ 0.067 for r 0 = 1.5 , J = 0.05 , 0.060 for r 0 = 2.0 , J = 0.08 , and 0.058 for r 0 = 2.5 , J = 0.12 . Photon orbits are analyzed using five redshift functions, yielding critical impact parameters with prograde-retrograde splitting characterized by an asymmetry parameter D between 0.02 and 0.09, compared to D K e r r ∼ 0.06 to 0.15 for Kerr black holes. The shadow scale satisfies R sh / r 0 ∼ 1.2 to 1.8, with Lorentzian shadows 5% to 12% larger than Gaussian ones. The photon-ring thickness is Δ R ph / r 0 ∼ 0.05 to 0.25. The weak energy condition holds everywhere, while null energy condition violation is localized within Δ r ex / r 0 ∼ 0.1 to 0.4. The volume-integral quantifier gives I V ( G ) ∼ − 0.012 and I V ( L ) ∼ − 0.036 for M = 2.5 , r 0 = 2.0 , l = 0.3 . Wormhole shadows are 4% to 10% smaller and half as asymmetric as Kerr shadows, offering potential observational discriminants for next-generation interferometry.

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