A Calabi-Yau threefold coming from two black holes

Abstract

In this paper, we show that a set of six square roots of homogeneous polynomials in four variables, related to a binary system of black holes studied by Stefan Weinzierl, is not rationalizable. We prove it by showing that the variety $X$ associated to the product of four of the six square roots is not unirational. In particular, we show that the smooth model of $X$ is a Calabi-Yau threefold.

V.2: Section 4 edited. Conjectures 4.25 and 4.31 changed. Exposition overall (hopefully) improved. Main results untouched. Comments still welcome