Chaos in charged AdS black hole extended phase space

M Chabab,H El Moumni,S Iraoui,K Masmar,S Zhizeh

doi:10.1016/j.physletb.2018.04.014

Abstract

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare–Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

Highlights

One of the crowning achievements of the Golden Age of General Relativity was the discovery that black holes exhibit thermodynamical properties, providing a comprehensive treatment of the study of their phase transitions [1]
One treats the cosmological constant as a thermodynamic variable in a so-called extended phase space the whole black hole system has been mapped to the van der Waals fluid system successfully in many avenues with the fact that the P − V diagram of the black holes at constant temperature and charges [2, 3] consolidating further the analogy between small/large black hole with the Van der Waals liquid/gas phase transitions [4, 5, 6, 7, 8, 9, 10, 11].These developments have once again put black holes at the center of theoretical physics
Having obtaining the essential features originating from the effect of a small periodic perturbation, where the temperature (25) is below the critical one, when the charged-AdS black hole is initially quenched in the unstable spinodal region, we will investigate the effects of small spatially periodic thermal variations of a Van der Waals-like black hole in (26) the equilibrium configuration

Summary

Chaos in charged AdS black hole extended phase space

M. Chabab a , ∗, H. El Moumni a,b , S. Iraoui a , K. Masmar a , S. Zhizeh a a High Energy and Astrophysics Laboratory, Physics Department, FSSM, Cadi Ayyad University, P.O.B. 2390 Marrakech, Morocco. b LMTI, Department of Physics, Faculty of Sciences, Ibn Zohr University, Agadir, Morocco.

Introduction

In this region the factor

Conclusion