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PreprintCC BY 4.0arXiv

Critical limits of accelerating Kerr--NUT spacetimes and the non-expanding Plebański--Demiański family

  • Kenneth Hong
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Abstract

We study degenerate-horizon limits of vacuum accelerating Kerr--NUT spacetimes with finite, nonzero NUT parameter. At cubic criticality, a2=m2+ℓ2 and αm=1, a projective coordinate transformation relates the complete critical parent metrics by a local homothety. The cubic horizon has one finite axis and a noncompact angular end, and its near-horizon limit is locally homothetic to the swirling universe. Explicit four-dimensional coordinate transformations place the ordinary extremal, Nariai and cubic near-horizon metrics in the negative-, positive- and zero-curvature longitudinal sectors of the non-expanding Plebański--Demiański family. The Nariai correspondence includes an exceptional endpoint that requires a separate Killing chart. Under a cubic-adapted near-critical scaling, fixed first-order separations between the approaching horizons do not affect the leading metric. The global Killing identifications and regular completion of the critical parent remain open.

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Cite

BibTeXRIS
BibTeX
@misc{hong2026critical,
  title = {{Critical limits of accelerating Kerr--NUT spacetimes and the non-expanding Plebański--Demiański family}},
  author = {Kenneth Hong},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25031},
  eprint = {2610.25031},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25031},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Critical limits of accelerating Kerr--NUT spacetimes and the non-expanding Plebański--Demiański family
AU  - Kenneth Hong
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25031
UR  - https://arxiv.org/abs/2610.25031
AB  - We study degenerate-horizon limits of vacuum accelerating Kerr--NUT spacetimes with finite, nonzero NUT parameter. At cubic criticality, a^2=m^2+ℓ^2 and αm=1, a projective coordinate transformation relates the complete critical parent metrics by a local homothety. The cubic horizon has one finite axis and a noncompact angular end, and its near-horizon limit is locally homothetic to the swirling universe. Explicit four-dimensional coordinate transformations place the ordinary extremal, Nariai and cubic near-horizon metrics in the negative-, positive- and zero-curvature longitudinal sectors of the non-expanding Plebański--Demiański family. The Nariai correspondence includes an exceptional endpoint that requires a separate Killing chart. Under a cubic-adapted near-critical scaling, fixed first-order separations between the approaching horizons do not affect the leading metric. The global Killing identifications and regular completion of the critical parent remain open.
ER  -