Spatial and Temporal Chaos of a Bardeen-AdS Black Hole and Effects of Quintessence Dark Energy
Abstract
Thermal chaos under spatially/temporally periodic perturbations in the extended phase space of Bardeen-AdS black holes surrounded by quintessence dark energy is investigated. The occurring condition of chaos is obtained with the Melnikov integral. It is shown that spatial chaos is always supposed to occur even for a tiny spatially periodic perturbation imposed on the equilibrium configuration. However, the temporal chaos will arise in the unstable spinodal region only if the given perturbed amplitude γ is larger than a critical value γc. The value of γc is determined by the magnetic monopole charge eta, the initial temperature T0, the quintessence state parameter ω, and the quintessence normalization parameter a. Particularly, combining the effects of ω and a together, we find that the quintessence appears quite similar to an enhancing/damped mechanism. In other words, there exists a critical value hoc of the quintessence dark energy density ho. In the region of ho < hoc, the existence of quintessence leads to a reduction in the viscosity of black holes and thus makes the system more likely to exhibit chaotic behavior. Conversely, given the energy density ho > hoc, the system acquires higher viscosity so that it is endowed with the ability to endure a larger thermal fluctuation.