Toward a holographic theory for general spacetimes

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.

Towards bulk metric reconstruction from extremal area variations

“…Our result is purely geometric, and applies to any geometry with finite boundary ∂M : in other words, whenever the aforementioned boundary data is known (including most importantly the areas of two-dimensional spacelike extremal surfaces anchored to ∂M ), so is the metric in the region R. Indeed, it has been suggested (though we remain agnostic on this topic) that this boundary data might be available for holographic screens in the program of generalized holography [87,88]; if true, our result would apply.…”

Areas and entropies in BFSS/gravity duality

“…12 11 Alternatively, we can work in the un-gauged model and consider all the operators that appear here. 12 One natural choice [53] is to normalize the spherical harmonics and matrix spherical harmonics as 1 N trΦ † l,m Φ l,m = 1, 1 4π d 2 xY * l,m Y l,m = 1 and set c l = 1. Another natural choice is to define unit-normalized vectors v n withn · Jv n = Jv n (where J = (N − 1)/2), and define the map from matrix fluctuations to functions as δM → f δM where f δM (n) = v † n δM v n .…”

“…1 It is interesting to ask whether other extremal surfaces (or more general classes of surfaces) have an interpretation in terms of entropy. Various investigations along these lines have appeared in the past, for example [9][10][11][12].…”

New constraints for holographic entropy from maximin: A no-go theorem

“…However, [19] suggested a possibility: that 7 By a realistic spacetime we mean one satisfying conditions given in [12] which include the null curvature condition. 8 We focus on the screen entanglement proposal because it is a generalization of the HRT formula that has many desirable features [15,16]. Our considerations here apply, however, to any reasonable extension of covariant holographic entanglement entropy to general spacetimes like that of [17].…”