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arXiv · 2602.15764

Quantitative local recovery of Kerr-de Sitter parameters from high-frequency equatorial quasinormal modes

Ruiliang Li
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Abstract

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 $\Lambda>0$), 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 $\Lambda$ 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 $(M,a,\Lambda)$ locally in the slow-rotation regime away from $a=0$.

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Ruiliang Li. 2026-02-17. Quantitative local recovery of Kerr-de Sitter parameters from high-frequency equatorial quasinormal modes. https://arxiv.org/abs/2602.15764

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