Bulk reconstruction of metrics inside black holes by complexity

Hashimoto, Koji; Watanabe, Ryota

doi:10.1007/jhep09(2021)165

Cited by 9 publications

(3 citation statements)

References 80 publications

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“…Entanglement measures are by far not the only data with which one can reconstruct the bulk geometry; work in this direction include [30,[52][53][54][55][56]. Other quantities that have been investigated in the literature include operators [57,58], four-point correlators [59], differential entropy [60,61], fidelity [62], complexity [63], light-cone cuts [64,65], chiral condensate [66,67], conductivity [68], hadron spectra [69], and magnetization [70] with varying degree of assumptions about the dual classical bulk gravity. To all of these cases one could incorporate the Hamiltonian Monte Carlo approach discussed in Sec.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Holographic spacetime from lattice Yang-Mills theory

et al. 2022

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Entanglement entropy is a notoriously difficult quantity to compute in strongly interacting gauge theories. Existing lattice replica methods have suffered from a severe signal-to-noise ratio problem, making high-precision studies prohibitively expensive. Our improved lattice method mitigates this situation and allows us to probe holographic predictions for the behavior of entanglement entropies in three- and four-dimensional Yang-Mills theories. We use this data for the numerical reconstruction of holographic bulk metrics.

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Section: Discussion and Outlookmentioning

confidence: 99%

Holographic spacetime from lattice Yang-Mills theory

et al. 2022

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“…As another question, how deep into the bulk can cuts and point functions describe? The only investigation of reconstructing the metric inside a black hole is proposed in [21] by using complexity, and here we would like to discuss the possibility of doing it in our framework. Let us first consider the potential of point functions.…”

Section: Summary and Discussionmentioning

confidence: 99%

Light-cone cuts and hole-ography: explicit reconstruction of bulk metrics

Takeda

2021

Preprint

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In this paper, the two reconstruction methods, light-cone cuts method and hole-ography, are combined to provide complete bulk metrics of asymptotically AdS 3 static spacetimes. As examples, our method is applied to the geometries of pure AdS 3 , AdS 3 soliton, and BTZ black hole, and we see them successfully reconstructed. The light-cone cuts method is known to have difficulty in obtaining conformal factors, while the holeography in describing temporal components. Combining the two methods, we overcome the disadvantages and give complete metrics for a class of holographic theories such that entanglement wedge and causal wedge coincide. Light-cone cuts are identified by entanglement entropy in our method. We expect our study to lead to the discovery of a universal relation between the two methods, by which the combination would be applied to more generic cases.

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“…This is the essence of the program of 'bulk reconstruction' (see, e.g., [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][173][174][175][176]), which aims to build the bulk metric purely from boundary data, typically field theory entanglement, by inverting some differential operator encoding information about bulk metric perturbations. Since complexity describes the interior geometry of black holes, reconstruction of the geometry inside of a horizon should be possible starting from complexity, as was recently carried out in [177], where input knowledge of the time derivatives of complexity and the Hartman-Maldacena entanglement entropy, and the metric outside of the horizon is required. More generally, from the perspective pursued in this article, we would start with a manifold M with boundary ∂M , and a set of forms δu which encode the local details of complexity associated with timelike boundary subregions.…”

Section: Jhep02(2022)093mentioning

confidence: 99%

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity

Pedraza

Russo

Svesko

et al. 2022

J. High Energ. Phys.

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Holographic entanglement entropy was recently recast in terms of Riemannian flows or ‘bit threads’. We consider the Lorentzian analog to reformulate the ‘complexity=volume’ conjecture using Lorentzian flows — timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. By the nesting of Lorentzian flows, holographic complexity is shown to obey a number of properties. Particularly, the rate of complexity is bounded below by conditional complexity, describing a multi-step optimization with intermediate and final target states. We provide multiple explicit geometric realizations of Lorentzian flows in AdS backgrounds, including their time-dependence and behavior near the singularity in a black hole interior. Conceptually, discretized flows are interpreted as Lorentzian threads or ‘gatelines’. Upon selecting a reference state, complexity thence counts the minimum number of gatelines needed to prepare a target state described by a tensor network discretizing the maximal volume slice, matching its quantum information theoretic definition. We point out that suboptimal tensor networks are important to fully characterize the state, leading us to propose a refined notion of complexity as an ensemble average. The bulk symplectic potential provides a specific ‘canonical’ thread configuration characterizing perturbations around arbitrary CFT states. Consistency of this solution requires the bulk satisfy the linearized Einstein’s equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating for a principle of ‘spacetime complexity’. Lastly, we argue Lorentzian threads provide a notion of emergent time. This article is an expanded and detailed version of [1], including several new results.

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Bulk reconstruction of metrics inside black holes by complexity

Abstract: We provide a formula to reconstruct bulk spacetime metrics inside black holes by the time dependence of complexity in the dual quantum field theory, based on the complexity=volume (CV) conjecture in the holographic duality.

Cited by 9 publications

References 80 publications

Holographic spacetime from lattice Yang-Mills theory

Holographic spacetime from lattice Yang-Mills theory

Light-cone cuts and hole-ography: explicit reconstruction of bulk metrics

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity

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