# Recovering the spacetime metric from a holographic dual

@article{Engelhardt2016RecoveringTS, title={Recovering the spacetime metric from a holographic dual}, author={Netta Engelhardt and Gary T. Horowitz}, journal={arXiv: High Energy Physics - Theory}, year={2016} }

We review our recent proposal to use certain spatial cross-sections of the boundary at infinity -- light-cone cuts -- to recover the conformal metric in the bulk. We discuss some extensions of this work, including how to obtain the conformal metric near the horizon of a collapsing black hole. We also show how to obtain the conformal factor under certain conditions.

## 24 Citations

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## References

SHOWING 1-10 OF 39 REFERENCES

Towards a Reconstruction of General Bulk Metrics

- Mathematics
- 2017

We prove that the metric of a general holographic spacetime can be reconstructed (up to an overall conformal factor) from distinguished spatial slices - "light-cone cuts" - of the conformal boundary.…

Holographic representation of local bulk operators

- Mathematics
- 2006

The Lorentzian anti-de Sitter/conformal field theory correspondence implies a map between local operators in supergravity and nonlocal operators in the CFT. By explicit computation we construct CFT…

Constructing local bulk observables in interacting AdS/CFT

- Physics, Mathematics
- 2011

Local operators in the bulk of anti-de Sitter can be represented as smeared operators in the dual conformal field theory. We show how to construct these bulk observables by requiring that the bulk…

Equivalent equations of motion for gravity and entropy

- Physics, Geology
- 2016

A bstractWe demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so,…

String scattering in flat space and a scaling limit of Yang-Mills correlators

- Physics, Mathematics
- 2011

We use the flat space limit of the AdS/CFT correspondence to derive a simple relation between the 2{yields}2 scattering amplitude of massless string states in type IIB superstring theory on…

Local bulk S-matrix elements and conformal field theory singularities

- Physics
- 2009

We give a procedure for deriving certain bulk S-matrix elements from corresponding boundary correlators. These are computed in the plane-wave limit, via an explicit construction of certain boundary…

Bulk-cone singularities & signatures of horizon formation in AdS/CFT

- Mathematics
- 2007

We discuss the relation between singularities of correlation functions and causal properties of the bulk spacetime in the context of the AdS/CFT correspondence. In particular, we argue that the…

Holographic Derivation of Entanglement Entropy from AdS/CFT

- Physics
- 2006

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal…

Looking for a bulk point

- Mathematics
- 2015

A bstractWe consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity…

Holographic holes in higher dimensions

- Physics
- 2014

A bstractWe extend the holographic construction of [1] from AdS3 to higher dimensions. In particular, we show that the Bekenstein-Hawking entropy of codimension-two surfaces in the bulk with planar…