Toward a Holographic Theory for General Spacetimes

TL;DR

This paper proposes a holographic framework for general spacetimes that does not depend on asymptotic regions, exploring entanglement structures and state selection in quantum gravity and cosmology.

Contribution

It introduces a holographic theory applicable to general spacetimes, analyzing entanglement and Hilbert space structures beyond AdS/CFT.

Findings

Holographic entanglement features differ from AdS/CFT but converge in certain limits.

Two plausible Hilbert space structures: direct sum and spacetime equals entanglement.

Discussion on quantum gravity state selection, including the multiverse.

Abstract

We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct sum and "spacetime equals entanglement" structure. The former preserves a naive relationship between linear operators and observable quantities, while the latter respects a more direct connection between holographic entanglement and spacetime. We also discuss the issue of selecting a state in quantum gravity, in particular how the state of the multiverse may be selected in the landscape.