Emergence of Calabi–Yau manifolds in high-precision black-hole scattering
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…
Read the paper
Related studies
- A Survey on Knowledge Graphs: Representation, Acquisition, and Applications
- Toxicity of nanomaterials
- The Human Gene Mutation Database: towards a comprehensive repository of inherited mutation data for medical research, genetic diagnosis and next-generation sequencing studies
- Halogen bonding (X‐bonding): A biological perspective
- Biofilm formation at the air–liquid interface by the Pseudomonas fluorescens SBW25 wrinkly spreader requires an acetylated form of cellulose
- Opioid Activation of Toll-Like Receptor 4 Contributes to Drug Reinforcement
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.