Photon spheres, elliptic surfaces, and Seiberg-Witten geometry

Source abstract

We study null geodesics in Reissner-Nordström-de Sitter spacetime and in its $ω=-2/3$ Kiselev deformation through the elliptic curves defined by the radial equation. The relation of these curves to the non-critical $E_7$ Seiberg-Witten family yields differential equations for finite-distance light deflection, and explains the boundary source term through a suitable gauge of the Seiberg-Witten differential. This geometry separates the extremal point $Q^2=M^2$ from the Argyres-Douglas point $Q^2=9M^2/8$. We also determine the Kiselev critical and horizon loci, and show that, at fixed nonzero angular momentum, the Argyres-Douglas and ultracold loci meet only at zero Killing energy.