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arXiv · 2512.05003

Schwarzschild Black Hole Turbulence: Scalar Probe

Alex Kehagias·Antonio Riotto
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Abstract

We explore how perturbations of a Schwarzschild black hole can redistribute energy among scalar modes and seed turbulent like cascades. We make use of the van der Pol-Krylov-Bogoliubov averaging method and derive coupled mode equations that describe near-resonant interactions between neighbouring multipoles. We compare two routes to instability, namely the difference-frequency mixing between adjacent modes and the diagonal (Mathieu) self-modulation channel. We show that, at high multipole number (eikonal limit), the difference-frequency route dominates and drives a one-way cascade from higher to lower frequencies. We chart the corresponding instability regions ("tongues") and quantify their detuning dependence. The framework provides a simple, quantitative mechanism for energy transfer in black hole ringdowns and clarifies when and how turbulent signatures can arise within linear probes on a weakly perturbed background.

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Alex Kehagias, Antonio Riotto. 2025-12-04. Schwarzschild Black Hole Turbulence: Scalar Probe. https://arxiv.org/abs/2512.05003

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