Cold kinetic theory is not cold fluid theory: A collective mode in self-gravitating spheres

Mikael Tacu

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arXiv · 2606.23068

Cold kinetic theory is not cold fluid theory: A collective mode in self-gravitating spheres

Mikael Tacu

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Abstract

Cold collisionless matter is usually described by pressureless fluid equations; this fails in three-dimensional spherical geometry. For the cold spherical case, kinetic and fluid descriptions share the same time-domain dynamics, but if we look at the spectrum, the kinetic system admits one solution the fluid does not: a discrete mode at twice the central orbital frequency, $\omega_0 = 2\Omega(0)$. It is specific to 3D: razor-thin disks reduce to the fluid description. Nonlinear simulations confirm it survives at finite dispersion. Around Sgr~A$^*$ it lies at $\kappa(r_{\rm in})$, with $r_{\rm in}$ the cusp's inner edge; if excited, stars at all radii would oscillate at this one frequency.

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Mikael Tacu. 2026-06-22. Cold kinetic theory is not cold fluid theory: A collective mode in self-gravitating spheres. https://arxiv.org/abs/2606.23068

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