Quantitative local recovery of Kerr-de Sitter parameters from high-frequency equatorial quasinormal modes
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915802558496768 |
|---|---|
| author | Li, Ruiliang |
| author_facet | Li, Ruiliang |
| contents | We study an inverse resonance problem for the scalar wave equation on the Kerr-de Sitter family. In a compact subextremal slow-rotation regime and at a fixed overtone index, high-frequency quasinormal modes admit semiclassical quantization and a real-analytic labeling by angular momentum indices. Using this structure, we first prove that a finite equatorial high-frequency package of quasinormal-mode frequencies determines the mass and rotation parameter $(M,a)$ (for fixed cosmological constant $Λ>0$), with a quantitative stability estimate. As a key geometric input we compute explicit second-order (in $a$) corrections to the equatorial photon-orbit invariants which control the leading real and imaginary parts of the quasinormal modes. Finally, allowing $Λ$ to vary in a compact interval, we show that adding one damping observable (the scaled imaginary part of a single equatorial mode) yields a three-parameter inverse theorem: a finite package of three independent real observables determines $(M,a,Λ)$ locally in the slow-rotation regime away from $a=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative local recovery of Kerr-de Sitter parameters from high-frequency equatorial quasinormal modes Li, Ruiliang Mathematical Physics General Relativity and Quantum Cosmology Analysis of PDEs 35P25 (Primary) 35R30, 58J50, 83C57 (Secondary) We study an inverse resonance problem for the scalar wave equation on the Kerr-de Sitter family. In a compact subextremal slow-rotation regime and at a fixed overtone index, high-frequency quasinormal modes admit semiclassical quantization and a real-analytic labeling by angular momentum indices. Using this structure, we first prove that a finite equatorial high-frequency package of quasinormal-mode frequencies determines the mass and rotation parameter $(M,a)$ (for fixed cosmological constant $Λ>0$), with a quantitative stability estimate. As a key geometric input we compute explicit second-order (in $a$) corrections to the equatorial photon-orbit invariants which control the leading real and imaginary parts of the quasinormal modes. Finally, allowing $Λ$ to vary in a compact interval, we show that adding one damping observable (the scaled imaginary part of a single equatorial mode) yields a three-parameter inverse theorem: a finite package of three independent real observables determines $(M,a,Λ)$ locally in the slow-rotation regime away from $a=0$. |
| title | Quantitative local recovery of Kerr-de Sitter parameters from high-frequency equatorial quasinormal modes |
| topic | Mathematical Physics General Relativity and Quantum Cosmology Analysis of PDEs 35P25 (Primary) 35R30, 58J50, 83C57 (Secondary) |
| url | https://arxiv.org/abs/2602.15764 |