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PreprintCC BY 4.0arXiv

Hyperboloidal Initial Data with Prescribed Asymptotic Charges

  • Károly Csukás
  • János Östör
  • István Rácz
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Abstract

A novel method is introduced for constructing hyperboloidal initial data with direct analytic control over asymptotic charges prior to solving the Einstein constraint equations. Using the parabolic-hyperbolic formulation of the constraints together with a Fuchsian-analysis-inspired spectral solver, the asymptotic degrees of freedom, which determine infinite towers of asymptotic charges, including the Bondi energy and angular momentum, are used to prescribe the asymptotic behavior of solutions. As a proof of concept, we explicitly construct hyperboloidal initial data for a spinning black hole with Bondi energy EB = 2 and angular momentum JB = 1/2, starting from seed data induced on a hyperboloidal slice of the non-rotating Schwarzschild spacetime with mass M=1.

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Cite

BibTeXRIS
BibTeX
@misc{csukas2026hyperboloidal,
  title = {{Hyperboloidal Initial Data with Prescribed Asymptotic Charges}},
  author = {Károly Csukás and János Östör and István Rácz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33266},
  eprint = {2610.33266},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33266},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hyperboloidal Initial Data with Prescribed Asymptotic Charges
AU  - Károly Csukás
AU  - János Östör
AU  - István Rácz
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33266
UR  - https://arxiv.org/abs/2610.33266
AB  - A novel method is introduced for constructing hyperboloidal initial data with direct analytic control over asymptotic charges prior to solving the Einstein constraint equations. Using the parabolic-hyperbolic formulation of the constraints together with a Fuchsian-analysis-inspired spectral solver, the asymptotic degrees of freedom, which determine infinite towers of asymptotic charges, including the Bondi energy and angular momentum, are used to prescribe the asymptotic behavior of solutions. As a proof of concept, we explicitly construct hyperboloidal initial data for a spinning black hole with Bondi energy E_B = 2 and angular momentum J_B = 1/2, starting from seed data induced on a hyperboloidal slice of the non-rotating Schwarzschild spacetime with mass M=1.
ER  -