https://arxiv.org/abs/1712.02803(adsbygoogle = window.adsbygoogle || []).push({});

Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space

ChunJun Cao, Sean M. Carroll

(Submitted on 7 Dec 2017)

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how Radon transforms can be used to convert this data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

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# Condensed matter physics, area laws & LQG?

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