Holographic integral geometry with time dependence

Abstract

We write down Crofton formulas--expressions that compute lengths of spacelike curves in asymptotically AdS${}_3$ geometries as integrals over kinematic space--which apply when the curve and/or the background spacetime is time-dependent. Relative to their static predecessor, the time-dependent Crofton formulas display several new features, whose origin is the local null rotation symmetry of the bulk geometry. In pure AdS${}_3$ where null rotations are global symmetries, the Crofton formulas simplify and become integrals over the null planes, which intersect the bulk curve.

arXiv comment21 pages plus references, 6 figures

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Cited by in corpus (9)

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• Topological shadows and complexity of islands in multiboundary wormholes
• Bit threads, Einstein's equations and bulk locality
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
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• Boundary and bulk notions of transport in the AdS${}_3$/CFT${}_2$ correspondence
• Cost of holographic path integrals
• Bulk reconstruction of AdS${}_{d+1}$ metrics and developing kinematic space