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Mode stability for the Klein-Gordon equation on subextremal Kerr-de Sitter spacetimes

  • Peter Hintz
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Abstract

We prove mode stability for the Klein-Gordon equation on Kerr-de Sitter black hole spacetimes in the full subextremal range and for the range mKG2∈[0,Λ√2] of squared scalar field masses that includes, in particular, the minimally coupled case mKG=0 and the conformally coupled case mKG2=2/3Λ (i.e., the Teukolsky equation for spin $0$). In combination with recent work by Petersen-Vasy, this proves, unconditionally, that sufficiently regular solutions of the scalar wave equation decay exponentially fast to constants, and in fact to zero for nonzero mKG.

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Cite

BibTeXRIS
BibTeX
@misc{hintz2026mode,
  title = {{Mode stability for the Klein-Gordon equation on subextremal Kerr-de Sitter spacetimes}},
  author = {Peter Hintz},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.25868},
  eprint = {2608.25868},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.25868},
}
RIS
TY  - UNPB
TI  - Mode stability for the Klein-Gordon equation on subextremal Kerr-de Sitter spacetimes
AU  - Peter Hintz
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.25868
UR  - https://arxiv.org/abs/2608.25868
AB  - We prove mode stability for the Klein-Gordon equation on Kerr-de Sitter black hole spacetimes in the full subextremal range and for the range m_KG^2∈[0,Λ√2] of squared scalar field masses that includes, in particular, the minimally coupled case m_KG=0 and the conformally coupled case m_KG^2=2/3Λ (i.e., the Teukolsky equation for spin $0$). In combination with recent work by Petersen-Vasy, this proves, unconditionally, that sufficiently regular solutions of the scalar wave equation decay exponentially fast to constants, and in fact to zero for nonzero m_KG.
ER  -