Relaxation of a Vlasov gas to an inhomogeneous state due to phase space mixing in an axisymmetric potential: A Newtonian analogy of the Kerr orbital motion
Abstract
We explore the dynamics of a Vlasov gas propagating in an external axisymmetric potential consisting of a central potential with an additional quadrupolar component which gives rise to two potential wells along the symmetry axis. Employing independently N-particle simulations and statistical methods, we show that an initially homogeneous and isotropic configuration evolves to an inhomogeneous final state with overdensities located at the wells. The quadrupolar component is chosen such that the equations of motion form an integrable Hamiltonian system, which allows one to compute the final state of the gas analytically. On the one hand, this allows one to compare the late-time behaviour of the simulations with an analytic prediction and on the other hand to understand the relaxation process through phase space mixing. Our model constitutes a Newtonian analogue of the particle motion in a Kerr spacetime, and we discuss possible applications to recently observed astrophysical phenomena.
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BibTeX
@misc{garciaperciante2026relaxation,
title = {{Relaxation of a Vlasov gas to an inhomogeneous state due to phase space mixing in an axisymmetric potential: A Newtonian analogy of the Kerr orbital motion}},
author = {Ana Laura García-Perciante and Merce Guerrero and Darío Núñez and Olivier Sarbach},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06913},
eprint = {2610.06913},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06913},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relaxation of a Vlasov gas to an inhomogeneous state due to phase space mixing in an axisymmetric potential: A Newtonian analogy of the Kerr orbital motion
AU - Ana Laura García-Perciante
AU - Merce Guerrero
AU - Darío Núñez
AU - Olivier Sarbach
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.06913
UR - https://arxiv.org/abs/2610.06913
AB - We explore the dynamics of a Vlasov gas propagating in an external axisymmetric potential consisting of a central potential with an additional quadrupolar component which gives rise to two potential wells along the symmetry axis. Employing independently N-particle simulations and statistical methods, we show that an initially homogeneous and isotropic configuration evolves to an inhomogeneous final state with overdensities located at the wells. The quadrupolar component is chosen such that the equations of motion form an integrable Hamiltonian system, which allows one to compute the final state of the gas analytically. On the one hand, this allows one to compare the late-time behaviour of the simulations with an analytic prediction and on the other hand to understand the relaxation process through phase space mixing. Our model constitutes a Newtonian analogue of the particle motion in a Kerr spacetime, and we discuss possible applications to recently observed astrophysical phenomena.
ER -