Abstract
We investigate the evolution of the mutual information between two spatial subsystems in a compact 1+1 dimensional CFT after a quantum quench. To this end, we use the dual holographic process, given by the 2+1 dimensional Vaidya-BTZ spacetime in global coordinates, which describes the collapse of a spherically symmetric null shell. So, we first discuss the spacelike geodesic structure of this geometry and then we present the various behaviors of the holographic mutual information observed in this case. We also consider the analogous process in the adiabatic limit and compare these two cases from a geometrical point of view.
Highlights
Been made using QFT techniques, this problem became more tractable with the appearance of the proposal that certain strongly coupled d-dimensional quantum field theories with a large number of degrees of freedom are dual to classical gravity theories in d + 1 dimensions
We first discuss the spacelike geodesic structure of this geometry and we present the various behaviors of the holographic mutual information observed in this case
It makes sense that the process of gravitational collapse ending in a black hole in an asymptotically AdSd+1 spacetime geometry is dual to thermalization in a CFT
Summary
We can see that t is identified with the static time coordinate ti inside the shell (i.e. for v < 0), but not with the static time to outside the shell, which makes sense since the Vaidya-BTZ spacetime is not static. In these new coordinates, infalling null geodesics always form angles of π/4 in ρ − t diagrams, whereas this is true for outgoing null geodesics only in the AdS part v < 0. More details about the structure of this spacetime can be found in [24]
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