Looking through the Kerr disk

We study null geodesics that connect the two asymptotically flat regions of the maximally extended Kerr spacetime. These vortical geodesics traverse both horizons and pass through the ring singularity, linking the positive- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>r</a:mi> </a:math> exterior to the negative- <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>r</c:mi> </c:math> asymptotic side. Using impact parameters, we identify a closed subset of parameter space, the inner throat, where the radial potential has no real roots, and photons exhibit no radial turning points. In this region, at most two constant-latitude geodesics exist, one of which is aligned with the principal null direction. We also identify the forbidden polar-angle band that limits the range of geodesics reaching an asymptotic observer. We solve the geodesic equations analytically and numerically in Eddington-Finkelstein-like coordinates, obtaining mutually consistent results that correct and extend previously available formulas. The resulting trajectories are used to construct simulated views for an observer in the negative- <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>r</e:mi> </e:math> domain, revealing strong image distortion and inversion, with possible implications for analogous white hole configurations.