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Abstract

We extend the Rioseco and Sarbach model into Reissner-Nordstr\"{o}m black hole accretes degenerate relativistic Fermi gas. The accretion theory is based on the Boyer-Lindquist coordinates and the Fermi gas follows Fermi-Dirac statistics at infinity. The expressions for the particle current density, the stress energy-momentum tensor, and three accretion rates are derived. We first investigated the impact of Risoseco and Sarbach model on the evolution of a black hole's charge. The results show that both the mass accretion rate and charge accretion rate are proportional to the particle accretion rate. We have also provided analytical results at infinity and numerical results within a finite range for these quantities. Our results indicate that the accretion rate decreases as the charge of the black hole increases, suggesting that our accretion model does not violate the cosmic censorship hypothesis. In this paper, we first point out that the accretion of Vlasov gas behaves as an anisotropic fluid containing two perfect-fluid components. One component represents the isotropic fluid of Fermi gas, while the other represents a null fluid. When using the Boyer-Lindquist coordinate system, we observed that the contribution from the null fluid persists even at infinity, which led to the radial pressure always smaller than the tangential pressure. Therefore, it's not appropriate to treat the accretion model as a perfect fluid at infinity.