Dark matter induced accretion dynamics and simulation around a non-commutative Schwarzschild black hole

In this paper, we are testing the accretion dynamics of test fluids in the spacetime of a newly proposed black hole (BH) solution. We begin by presenting the BH metric and systematically examining its geometric and structural properties that are directly relevant for accretion processes. The exact analytical solutions for fluid accretion are derived, and their physical validity is carefully assessed. We perform a comprehensive dynamical system analysis, including the identification and classification of sonic points, and apply the formalism to isothermal fluids. The behavior of accretion flows is additionally examined through the Hamiltonian dynamical system approach across various fluid types, including ultra-stiff, ultra-relativistic, radiation, and sub-relativistic regimes. Under these conditions, the corresponding plots and phase-space representations illustrate the effects of BH parameters on the flow dynamics. The analysis is then extended to fluids following a polytropic EoS, and the physical implications of the mass accretion rate are thoroughly discussed. In addition, we perform general relativistic hydrodynamics (GRHD) simulations to validate the analytical predictions. The numerical results confirm the existence of steady transonic accretion, the formation of shock structures, and the sensitivity of the flow morphology and accretion efficiency to the non-commutative parameters. Overall, the simulations provide a consistent and self-contained description of fluid accretion in the proposed BH spacetime, with implications for both theoretical studies and astrophysical modeling.