PreprintCC BY 4.0arXiv
Photon spheres, elliptic surfaces, and Seiberg-Witten geometry
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 E7 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 Q2=M2 from the Argyres-Douglas point Q2=9M2/8. 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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BibTeX
@misc{blankenship2026photon,
title = {{Photon spheres, elliptic surfaces, and Seiberg-Witten geometry}},
author = {Cordell Blankenship and Andreas Malmendier and Michael T. Schultz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30730},
eprint = {2609.30730},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30730},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Photon spheres, elliptic surfaces, and Seiberg-Witten geometry
AU - Cordell Blankenship
AU - Andreas Malmendier
AU - Michael T. Schultz
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30730
UR - https://arxiv.org/abs/2609.30730
AB - 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.
ER -