Abstract
In this paper, we will analyse the holographic complexity for time-dependent asymptotically $AdS$ geometries. We will first use a covariant zero mean curvature slicing of the time-dependent bulk geometries, and then use this co-dimension one spacelike slice of the bulk spacetime to define a co-dimension two minimal surface. The time-dependent holographic complexity will be defined using the volume enclosed by this minimal surface. This time-dependent holographic complexity will reduce to the usual holographic complexity for static geometries. We will analyse the time-dependence as a perturbation of the asymptotically $AdS$ geometries. Thus, we will obtain time-dependent asymptotically $AdS$ geometries, and we will calculate the holographic complexity for such a time-dependent geometries.
Highlights
An observation made from different branches of physics is that the physical laws can be represented by informational theoretical processes [1,2]
In this formalism, first a maximal spacelike slice of the bulk geometry is obtained though the mean curvature slicing, and a minimal surface γAt is constructed on this spacelike slice [26]
Just as the holographic entanglement entropy is dual to an area in the bulk of an anti-de Sitter (AdS) spacetime, holographic complexity is as a quantity dual to a volume in the bulk AdS
Summary
An observation made from different branches of physics is that the physical laws can be represented by informational theoretical processes [1,2]. A co-dimension one spacelike foliation of time-dependent asymptotically AdS geometry can be performed, and on such a spacelike slice the metric is spacelike, and a co-dimension two minimal surface can be defined on such a spacelike slice In this formalism, first a maximal spacelike slice of the bulk geometry is obtained though the mean curvature slicing, and a minimal surface γAt is constructed on this spacelike slice [26]. We will get a co-dimension one surface with a spacelike metric, and we will again define a co-dimension two minimal surface γAt on this spacelike slice of the bulk geometry It will be the same minimal surface which was used to calculate the time-dependent holographic entanglement entropy [26]. In this paper, we will analyze the time-dependent holographic complexity for such time-dependent geometries
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