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 (KN) spacetime, analyzing how spacetime symmetries constrain the distribution functions. The distribution function is shown to depend on the constants of motion ( m , E , L z , L ) and a configuration variable Q 3 . Furthermore, we discuss in detail the different scenarios of charged particles being captured or scattered by the black hole in KN spacetime, and analytically derive the boundaries of the absorption and scattering domains in phase space. Within the locally non-rotating frame, we compute particle number density, energy density, principal pressures, and construct a set of diagnostic parameters to quantitatively measure the anisotropy information of the Vlasov gas (relative to a perfect fluid), and provide the analytic results of these physical quantities at spatial infinity. In addition, we discuss the accretion rates of the KN black hole and obtain their analytic expressions. 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 absolute value of the normalized angular momentum accretion rate (which is negative) increases with a , and Q also moderately influences the angular momentum accretion rate through its effect on spacetime geometry. 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 spacetime geometries.