A Calabi-Yau threefold coming from two black holes

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.