Schwarzschild Black Hole Turbulence: Scalar Probe
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908694317367296 |
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| author | Kehagias, Alex Riotto, Antonio |
| author_facet | Kehagias, Alex Riotto, Antonio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_05003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schwarzschild Black Hole Turbulence: Scalar Probe Kehagias, Alex Riotto, Antonio General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Schwarzschild Black Hole Turbulence: Scalar Probe |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.05003 |