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Price's law for scalar waves on 1+4 dimensional subextremal Myers-Perry spacetimes

  • Pieter-Bart Peters
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Abstract

We consider Myers--Perry spacetimes (M,ga,b,m) in 1+4 dimensions with two spin parameters (a,b)∈ℝ2, which are a direct generalization of the well known Kerr spacetime in 1+3 dimensions. We prove that the Hamiltonian flow associated to ga,b,m−1 is normally hyperbolically trapped for the full subextremal range (|a|+|b|)2<2m. As an application, we prove a Price law with explicit leading order terms for solutions ϕ(t,x) of the scalar wave equation Boxga,b,mϕ=0 under the assumption of real mode stability. Our precise asymptotics imply that ϕ(t,x)=ct−3+𝒪(t−4+), where c∈ℂ is an explicitly computable constant.

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Cite

BibTeXRIS
BibTeX
@misc{peters2026prices,
  title = {{Price's law for scalar waves on 1+4 dimensional subextremal Myers-Perry spacetimes}},
  author = {Pieter-Bart Peters},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33812},
  eprint = {2610.33812},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33812},
}
RIS
TY  - UNPB
TI  - Price's law for scalar waves on 1+4 dimensional subextremal Myers-Perry spacetimes
AU  - Pieter-Bart Peters
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33812
UR  - https://arxiv.org/abs/2610.33812
AB  - We consider Myers--Perry spacetimes (M,g_a,b,m) in 1+4 dimensions with two spin parameters (a,b)∈ℝ^2, which are a direct generalization of the well known Kerr spacetime in 1+3 dimensions. We prove that the Hamiltonian flow associated to g_a,b,m^−1 is normally hyperbolically trapped for the full subextremal range (|a|+|b|)^2<2m. As an application, we prove a Price law with explicit leading order terms for solutions ϕ(t,x) of the scalar wave equation Box_g_a,b,mϕ=0 under the assumption of real mode stability. Our precise asymptotics imply that ϕ(t,x)=ct^−3+𝒪(t^−4+), where c∈ℂ is an explicitly computable constant.
ER  -