Chaos in Born–Infeld–AdS black hole within extended phase space

Born–Infeld–AdS black holes in extended phase space may possess phase structures resembling that of van der Waals fluid in four-dimensional spacetime. We study dynamics of its state, which is in the unstable spinodal region initially on phase space, under time-periodic thermal perturbations. By applying the Melnikov method, it is found that there exists a critical amplitude γc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma _c$$\end{document} of the perturbations, which depends on the Born–Infeld parameter b and the black hole charge Q, such that chaos occurs for γ>γc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma > \gamma _c$$\end{document}. We found that larger b or Q makes the onset of chaos easier. Space-periodic thermal perturbations on its equilibrium state are also studied and there is always chaos for whatever the perturbation amplitude is.