A discussion on the symmetry of relativistic Vlasov gas and its accretion in Kerr-Newman black hole

TL;DR

This paper analyzes the kinetic behavior of collisionless Vlasov gas around Kerr-Newman black holes, revealing how spacetime symmetries influence particle distributions and accretion rates, with implications for black hole evolution.

Contribution

It provides explicit expressions for particle densities and accretion rates in Kerr-Newman spacetime, highlighting the effects of black hole charge and rotation on plasma accretion.

Findings

Accretion rates decrease with increasing black hole charge and rotation.

Normalized angular momentum accretion rate increases with rotation but decreases with charge.

Weakly charged plasma tends to neutralize black holes and reduce angular momentum.

Abstract

We investigate the kinetic properties of collisionless Vlasov gas in Kerr-Newman spacetime, analyzing how spacetime symmetries constrain the distribution functions. The distribution function is shown to depend solely on the constants of motion ($m$, $E$, $L_z$, $L$), reflecting the complete integrability of the system. Within the Locally Non-Rotating Frame, we compute particle number density, energy density, principal pressures, and accretion rates, deriving explicit asymptotic expressions for J\"uttner-distributed plasma. Numerical results for the relative (normalized) mass and energy accretion rates reveal an identical parametric dependence: both are suppressed as the black hole's rotation $a$ and charge $Q$ increase. Conversely, the magnitude of the normalized angular momentum accretion rate (which is negative) increases with $a$ but decreases with $Q$. Accretion of weakly charged plasma drives charged black holes toward electrical neutrality while reducing angular momentum, ultimately favoring evolution toward Schwarzschild configurations. These findings provide new insights into kinetic accretion processes in extreme spacetime geometries.