Original title: Scalar quasinormal modes of Kerr--AdS$_{\bf 7}$ via accessory parameter expansions
Julián Barragán Amado · September 2026
Understanding how ripples travel around spinning black holes in higher dimensions is a tough math problem. Researchers studied scalar perturbationsSmall disturbances in a field that spreads uniformly in all directions., which are wave-like disturbances of a simple field, around a seven-dimensional Kerr--AdS black hole that spins in three independent ways. The wave equation splits into one radial equation and two angular equations, each having five regular singular pointsSpecific points in a differential equation where solutions behave in a controlled but complex way.. The researchers used a technique called the Hill determinant method to calculate analytic expansions for the accessory parametersAdditional constants needed to uniquely solve equations with multiple singular points. in two separate regimes. These mathematical expansions match results from the instanton part of the Nekrasov--Shatashvili function in four-dimensional quiver gauge theories. Using these expansions, they found perturbative formulas for angular eigenvalues when rotation is slow and for quasinormal mode frequencies for small black holes.
You are adjusting the strings on a harp where each string's tension affects the others. Changing one string alters the pitch of its neighbors, so you cannot tune it by working on strings in isolation. In this paper, the black hole's vibrations are like the harp strings, and the accessory parameters are like the tension adjustments that must match patterns from particle physics to solve the equations correctly.
This work connects black hole physics with quantum field theory, helping physicists test ideas for quantum gravity. It could influence how we understand the fundamental laws of the universe.
The work applies only to seven-dimensional Kerr-AdS black holes with three rotations and scalar perturbations. Results are derived in specific limits: slowly rotating and small black hole. It does not address other perturbation types, different dimensions, or general cases beyond these regimes.
Ask anything about this paper. Answers come from its abstract, and say so when the abstract doesn't cover your question.
Scalar quasinormal modes of Kerr--AdS$_{\bf 7}$ via accessory parameter expansions — Julián Barragán Amado
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.