Kinematic Space and Wormholes

Abstract

The kinematic space could play a key role in constructing the bulk geometry from dual CFT. In this paper, we study the kinematic space from geometric points of view, without resorting to differential entropy. We find that the kinematic space could be intrinsically defined in the embedding space. For each oriented geodesic in the Poincaré disk, there is a corresponding point in the kinematic space. This point is the tip of the causal diamond of the disk whose intersection with the Poincaré disk determines the geodesic. In this geometric construction, the causal structure in the kinematic space can be seen clearly. Moreover, we find that every transformation in the $SL(2,\mathbb{R})$ leads to a geodesic in the kinematic space. In particular, for a hyperbolic transformation defining a BTZ black hole, it is a timelike geodesic in the kinematic space. We show that the horizon length of the static BTZ black hole could be computed by the geodesic length of corresponding points in the kinematic space. Furthermore, we discuss the fundamental regions in the kinematic space for the BTZ blackhole and multi-boundary wormholes.

31 pages, 20 figures, published version

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Cited by in corpus (12)

• Topological Complexity in AdS3/CFT2
• Holographic Subregion Complexity from Kinematic Space
• Topological shadows and complexity of islands in multiboundary wormholes
• A defect in holographic interpretations of tensor networks
• Kinematic space and the orbit method
• Kinematic space for conical defects
• Holographic relations for OPE blocks in excited states
• Wormholes and holographic decoherence
• Berry curvature, horocycles and scattering states in $Ad{S}_3/CF{T}_2$
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Scanning space-time with patterns of entanglement
• Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure