Conformal-mapping method for horizon multipoles in numerical relativity: Implementation, Kerr validation, and applications beyond axisymmetry
Year: 2026
Type: article
Abstract: We present a numerical method that constructs geometrically defined coordinates on black-hole horizons, from which the multipole moments are computed without assuming axisymmetry. This method, which we denote the conformal-mapping method (CMM), provides a numerical realization of the conformal construction proposed by Ashtekar et al. in 2022, combining discrete Ricci flow, spectral embedding onto the unit sphere, and Möbius gauge fixing by the vanishing-area-dipole condition. We first test the CMM against analytic Kerr benchmarks, and then apply it to an equal-mass, non-spinning binary black-hole merger. We also compare it with an approximate-symmetry-based method. The CMM allows the multipole moments to be expressed in a fixed reference frame, whereas the symmetry-adapted frame can reorient abruptly when the preferred approximate axis changes. In a frame aligned with the orbital angular momentum, the amplitude of the quadrupole mode grows during inspiral and decays after merger, displaying a qualitative ringdown behavior. These results show that the CMM is a useful tool for studying horizon geometry in dynamical situations where no stable symmetry axis is available.
DOI: 10.1103/bdhs-3qt4
Authors: Yeong-Bok Bae, Young-Hwan Hyun, Gungwon Kang
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: National Research Foundation, Korea Institute of Science and Technology Information, Korea Astronomy and Space Science Institute, National Research Foundation of Korea, Ministry of Science and ICT, South Korea, National Supercomputing Center, Korea Institute of Science and Technology Information
OpenAlex ID: W7202170996