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

Abstract

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 ω q . 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 r c , separating thermodynamically stable from unstable phases. Interestingly, noncommutative effects shift r c to larger values, effectively expanding the stability region. In the optical domain, we find that the shadow radius increases as ω q 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 ω R increases with both α and Θ , while the damping rate ω I 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.