A Calabi-Yau threefold coming from two black holes

TL;DR

This paper demonstrates that a specific Calabi-Yau threefold, derived from a mathematical model related to black holes, is not rationalizable, revealing complex geometric properties of the associated variety.

Contribution

It establishes the non-rationalizability of a Calabi-Yau threefold linked to a binary black hole system, connecting algebraic geometry with black hole models.

Findings

The variety $X$ is not unirational.

The smooth model of $X$ is a Calabi-Yau threefold.

The associated variety cannot be rationalized.

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.