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arXiv · 2609.30730

Photon spheres, elliptic surfaces, and Seiberg-Witten geometry

Cordell Blankenship·Andreas Malmendier·Michael T. Schultz
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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.

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Cordell Blankenship, Andreas Malmendier, Michael T. Schultz. 2026-09-25. Photon spheres, elliptic surfaces, and Seiberg-Witten geometry. https://arxiv.org/abs/2609.30730

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