Holographic entanglement entropy for small subregions and thermalization of Born–Infeld AdS black holes

Applying the Born–Infeld Anti de Sitter charged black hole metric we calculate holographic entanglement entropy (HEE) by regarding the proposal of Ryu and Takanayagi. To do so we assume that time dependence of the black hole mass and charge to be as step function. Our work is restricted to small subregions where a collapsing null shell does not penetrate the black holes horizon. To calculate time dependent HEE we use perturbation method for small subregions where turning point is much smaller than local equilibrium point of black hole. We choose two shape functions for entangled regions on the boundary which are the strip and the ball regions. There is a saturation time at which the null shell grazes the turning point and the HEE reaches to its maximum value. In general, this work satisfies result of the works presented by Camelio et al. and Zeng et al. We must point out that they used equal time two-point correlation functions and Wilson loops instead of the entanglement entropy (EE) as non-local observable to study this thermalization by applying the numerical method.