Abstract
We study the onset of chaos due to temporal and spatially periodic perturbations in charged Gauss-Bonnet AdS black holes in extended thermodynamic phase space, by analyzing the zeros of the appropriate Melnikov functions. Temporal perturbations coming from a thermal quench in the unstable spinodal region of P-V diagram may lead to chaos when a certain perturbation parameter $\ensuremath{\gamma}$ saturates a critical value, involving the Gauss-Bonnet coupling $\ensuremath{\alpha}$ and the black hole charge $Q$. A general condition following from the equation of state is found, which can rule out the existence of chaos in any black hole. Using this condition, we find that the presence of charge is necessary for chaos under temporal perturbations. In particular, chaos is absent in neutral Gauss-Bonnet and Lovelock black holes in general dimensions. Chaotic behavior continues to exist under spatial perturbations, irrespective of whether the black hole carries a charge or not.
Highlights
Black hole solutions and their thermodynamics in general relativity have thrown up remarkable surprises and continue to be an intriguing area of research
We generalize this result to generic black holes systems which have an extended thermodynamic phase space description and starting from the equation of state, we find a new relation which can be used to rule out chaos
We studied the emergence of chaotic behavior under temporal and spatial perturbations in the spinodal region of charged and neutral Gauss-Bonnet black holes in extended thermodynamic phase space
Summary
Black hole solutions and their thermodynamics in general relativity have thrown up remarkable surprises and continue to be an intriguing area of research. We show that neutral Gauss-Bonnet black holes in five and higher dimensions, in contrast, do not show chaotic behavior under temporal perturbations, despite the fact that a Van der Waals type phase transition and PV criticality exists [57] We generalize this result to generic black holes systems which have an extended thermodynamic phase space description and starting from the equation of state, we find a new relation which can be used to rule out chaos.
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