Imprints of Quintessence on Thermodynamic, Geodesic Motions and Quasinormal Modes of Hayward Black Holes in 4D Einstein-Gauss-Bonnet gravity

We investigate four-dimensional Hayward regular black holes surrounded by quintessence within Einstein–Gauss–Bonnet gravity. By coupling nonlinear electrodynamics to four-dimensional Einstein–Gauss–Bonnet gravity in the presence of a quintessence field, we obtain an exact black hole solution and analyze its geometric and horizon structure. A critical value of the quintessence equation of state parameter is identified, separating distinct horizon configurations. The effects of the Gauss-Bonnet coupling and magnetic charge on the horizon radius are examined. We further explore the thermodynamic behavior, including mass, temperature, entropy, and heat capacity, and determine the conditions for local stability. The Hawking temperature exhibits a maximum, indicating phase transition behavior. Timelike geodesics are studied to characterize stable and unstable particle orbits. Using Event Horizon Telescope data for M87 * , we derive an indicative upper bound on the GaussBonnet coupling parameter within a simplified Schwarzschild-like limit of Einstein–Gauss–Bonnet gravity, which should not be interpreted as a direct constraint on the full Hayward–quintessence–EGB model. Finally, quasinormal modes are computed using the sixth-order WKB approximation, supported by time-domain integration, revealing how higher-curvature corrections and quintessence modify the oscillation frequencies and damping rates. These results demonstrate observable deviations from standard general relativistic and Hayward black holes.