Thermodynamics and circular motion in a 4D Einstein–Gauss–Bonnet black hole embedded in quintessence

This manuscript analyzes the thermodynamical behavior of 4D Einstein–Gauss–Bonnet (EGB) black holes embedded in quintessence matter through discussions of mass function, Hawking temperature, surface gravity, and entropy. The investigation examines the PV criticality of the EGB black hole, comparing its isotherms with those of a van der Waals fluid. It proposes an analogy to a liquid–gas phase transition, with the small black hole phase analogous to liquid and the large black hole phase analogous to gas. Additionally, we analyze the circular motion of a timelike particle around the black hole, considering constraints on the coupling constant’s sign and exploring characteristics like angular momentum, energy, the innermost stable circular orbit, photon sphere, and the stability of circular orbits. Furthermore, we use the Lyapunov exponent, a function of radial distance, to determine the stability of orbits, particularly in the context of particle orbits around a black hole in the curved spacetime.