Thermal chaos of a charged dilaton-AdS black hole in the extended phase space

Abstract

We have studied thermal chaotic behavior in the extended phase space for a charged dilaton-AdS black hole by Melnikov method and present the effect of dilaton parameter on the thermal chaos.Our result show that for the temporal perturbation the thermal chaos in the charged dilaton-AdS black hole occurs only if the perturbation amplitude is larger than certain a critical value, but for the spatially perturbation, the chaos always exists irrespective of perturbation amplitude.These behaviors are similar to those in other AdS black hole, which can be regarded as the common features of the static AdS black holes. Moreover, we also find that the critical temporal perturbation amplitude leading to chaos increases with the dilaton parameter and decreases with the charge. This means that under the temporal perturbation the presence of dilaton parameter makes the onset of chaos more difficult, which differs from that of the charge parameter.

Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space *

“…Hence, it is not difficult conclude that there always exist spatial chaos always occurs in the thermodynamic system of the Kerr-AdS black hole under the spatially periodic thermal perturbation. This result is in agreement with other AdS black holes [31][32][33][34]. In Fig.…”

“…Their results can help to understand the correlation between the chaotic behavior and the P V  diagram of black holes. Subsequently, their study were extended to other black holes, including charged or neutral Gauss-Bonnet AdS black holes [32], the Born-Infeld-AdS black hole [33], and the charged dilaton-AdS black hole [34].…”

Spatial and Temporal Chaos of a Bardeen-AdS Black Hole and Effects of Quintessence Dark Energy

“…The similar result has also been found in the van der Waals fluid [16] and other black hole solutions in Refs. [25][26][27][28]. But to be specific, the chaotic features of the v − v phase space that is plotted in Fig.…”

“…Similarities and differences on thermal chaos and the corresponding critical value are pointed out. Subsequently, other important generalizations have been carried out in the context of charged Gauss-Bonnet-AdS Black holes [26], Born-Infeld-AdS black holes [27] and charged dilaton-AdS black holes [28]. Among them, the dependence of the critical amplitude γ c on electric charge q, dimension n, and other parameters have been investigated.…”

Chaotic motion around a black hole under minimal length effects

“…The Melnikov method has been used to discuss the chaotic behavior of geodesic motion in black holes perturbed by gravitational waves [14,15], electromagnetic fields [16] and a thin disc [17]. Recently, chaos due to temporal and spatially periodic perturbations in charged AdS black holes has also been investigated via the Melnikov method [18][19][20][21].…”