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

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.