4D Einstein-Gauss-Bonnet Black Holes Surrounded by Quintessence in Noncommutative Spacetime

In this work, we study the properties of 4-dimensional Einstein-Gauss-Bonnet black holes surrounded by a quintessence field in a noncommutative spacetime. By deriving the corresponding metric solution, we analyze the horizon structure and reveal configurations with up to three distinct horizons, influenced by the Gauss–Bonnet coupling constant α, the noncommutativity parameter Θ, and the quintessence state parameter ωq. Our analysis reveals several important results. In the thermodynamic sector, the Hawking temperature exhibits a characteristic peak during black hole evaporation; increasing α lowers the temperature overall, while larger values of Θ reduce the height of the peak. Regarding stability, the heat capacity shows a phase transition at a critical radius rc, separating thermodynamically stable from unstable phases. Interestingly, noncommutative effects shift rc to larger values, effectively expanding the stability region. In the optical domain, we find that the shadow radius increases as ωq becomes more negative, while the energy emission rate decreases with rising α or Θ. Finally, in the study of quasinormal modes, we observe that the oscillation frequency ωR increases with both α and Θ, while the damping rate ωI decreases. As a result, the quality factor Q is enhanced, indicating longer-lived perturbations. Our findings highlight the rich interplay between higher-curvature corrections, noncommutative geometry, and dark energy in black hole physics.