On hyperboloidal foliations in the study of black hole quasinormal modes

Abstract In this work, we demonstrate that the hyperboloidal foliation technique, applied to the study of black hole quasinormal modes, where the spatial boundary is shifted from spacelike infinity to the future event horizon and null infinity, is effectively equivalent to the continued fraction approach, in which the asymptotic wave function typically diverges at both ends of spatial infinity. Specifically, a given hyperboloidal slicing, corresponding to a particular choice of coordinates, always uniquely determines a scheme for extracting the asymptotic form of the wave function at the spatial boundary. Owing to the mathematical equivalence, it follows that the efficiency and precision observed using the hyperboloidal approach should be attributed, not to avoiding the pathological behavior at the spatial boundaries, but primarily to other factors, such as the use of Chebyshev grids.

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Publication Details

Journal
The European Physical Journal C
Published
2026-01-22
DOI
https://doi.org/10.1140/epjc/s10052-026-15283-1
Citations
1
Primary Topic
Black Holes and Theoretical Physics
Type
article
Field-Weighted Citation Impact
27.96

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article

On hyperboloidal foliations in the study of black hole quasinormal modes

Xiao‐Mei Kuang, Wei‐Liang Qian, Jodin C. Morey, Ramin G. Daghigh et al.
1 citations
The European Physical Journal C
Black Holes and Theoretical Physics
27.96
article

On hyperboloidal foliations in the study of black hole quasinormal modes

Xiao‐Mei Kuang, Wei‐Liang Qian, Jodin C. Morey, Ramin G. Daghigh, Rui-Hong Yue, Guan-Ru Li, Michael D. Green, Shui-Fa Shen
article en
1 citations

Abstract

Abstract In this work, we demonstrate that the hyperboloidal foliation technique, applied to the study of black hole quasinormal modes, where the spatial boundary is shifted from spacelike infinity to the future event horizon and null infinity, is effectively equivalent to the continued fraction approach, in which the asymptotic wave function typically diverges at both ends of spatial infinity. Specifically, a given hyperboloidal slicing, corresponding to a particular choice of coordinates, always uniquely determines a scheme for extracting the asymptotic form of the wave function at the spatial boundary. Owing to the mathematical equivalence, it follows that the efficiency and precision observed using the hyperboloidal approach should be attributed, not to avoiding the pathological behavior at the spatial boundaries, but primarily to other factors, such as the use of Chebyshev grids.

The European Physical Journal CVol. 86(1)
Universidade de São Paulo (BR), Turan University (KZ), Le Moyne College (US), Yangzhou University (CN), Universidade Estadual Paulista (Unesp) (BR), Metropolitan State University (US)
Fundação de Amparo à Pesquisa do Estado de São Paulo, National Natural Science Foundation of China, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Universidade Estadual Paulista
Openalex Percentile: Top 1%
Black Holes and Theoretical Physics
27.96
DOIOpen Access PDFOpenAlex
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