德国柏林洪堡大学Jan Plefka团队近日研究了高精度黑洞散射中Calabi-Yau流形的出现。2025年5月14日出版的《自然》杂志发表了这项成果。

当宇宙中的两个大质量物体（黑洞、中子星或恒星）相互飞过时，它们的引力相互作用会改变它们的轨迹。在相关的束缚轨道系统（双星inspiral）中发射的引力波现在经常被引力波天文台探测到。理论物理学需要提供高精度模板，以利用即将到来的引力波观测站数据的前所未有的灵敏度和精度。受这一挑战的启发，人们已经开发了几种分析和数值技术来近似解决这个引力三体问题。尽管数值相对论是准确的，但快速生成大量引力波模板太耗时了。为此，还需要近似的分析结果。 

研究组报告了一个新的、最高精度的分析结果，用于牛顿引力耦合G中五阶黑洞或中子星散射相遇的散射角、辐射能量和反冲，假设两个质量存在层次结构。这是通过将对撞机中基本粒子散射的最先进技术修改为宇宙中的经典物理问题来实现的。

该结果表明，与Calabi-You（CY）流形相关的数学函数，即复曲面的2n维推广，出现在这些散射中辐射能量的解中。研究组预计，该分析结果将有助于开发新一代引力波模型，为此，需要通过解析延拓和强场再归纳向束缚态问题过渡。

附：英文原文

Title: Emergence of Calabi–Yau manifolds in high-precision black-hole scattering

Author: Driesse, Mathias, Jakobsen, Gustav Uhre, Klemm, Albrecht, Mogull, Gustav, Nega, Christoph, Plefka, Jan, Sauer, Benjamin, Usovitsch, Johann

Issue&Volume: 2025-05-14

Abstract: When two massive objects (black holes, neutron stars or stars) in our universe fly past each other, their gravitational interactions deflect their trajectories1,2. The gravitational waves emitted in the related bound-orbit system—the binary inspiral—are now routinely detected by gravitational-wave observatories3. Theoretical physics needs to provide high-precision templates to make use of unprecedented sensitivity and precision of the data from upcoming gravitational-wave observatories4. Motivated by this challenge, several analytical and numerical techniques have been developed to approximately solve this gravitational two-body problem. Although numerical relativity is accurate5,6,7, it is too time-consuming to rapidly produce large numbers of gravitational-wave templates. For this, approximate analytical results are also required8,9,10,11,12,13,14,15. Here we report on a new, highest-precision analytical result for the scattering angle, radiated energy and recoil of a black hole or neutron star scattering encounter at the fifth order in Newton’s gravitational coupling G, assuming a hierarchy in the two masses. This is achieved by modifying state-of-the-art techniques for the scattering of elementary particles in colliders to this classical physics problem in our universe. Our results show that mathematical functions related to Calabi–Yau (CY) manifolds, 2n-dimensional generalizations of tori, appear in the solution to the radiated energy in these scatterings. We anticipate that our analytical results will allow the development of a new generation of gravitational-wave models, for which the transition to the bound-state problem through analytic continuation and strong-field resummation will need to be performed.

DOI: 10.1038/s41586-025-08984-2

Source: https://www.nature.com/articles/s41586-025-08984-2