Coarse graining holographic black holes

Abstract

We expand our recent work on the outer entropy, a holographic coarsegrained entropy defined by maximizing the boundary entropy while fixing the classical bulk data outside some surface. When the surface is marginally trapped and satisfies certain "minimar" conditions, we prove that the outer entropy is exactly equal to a quarter the area (while for other classes of surfaces, the area gives an upper or lower bound). We explicitly construct the entropy-maximizing interior of a minimar surface, and show that it satisfies the appropriate junction conditions. This provides a statistical explanation for the area-increase law for spacelike holographic screens foliated by minimar surfaces. Our construction also provides an interpretation of the area for a class of non-minimal extremal surfaces.On the boundary side, we define an increasing simple entropy by maximizing the entropy subject to a set of "simple experiments" performed after some time. We show (to all orders in perturbation theory around equilibrium) that the simple entropy is the boundary dual to our bulk construction.

From black hole entropy to energy-minimizing states in QFT

“…In this section we review a classical geometric construction by Engelhardt and Wall (EW) [5,13]. In Sec.…”

“…We begin by fixing some notations and conventions; see Sec. 2 of [13] for details. Let σ be a Cauchy splitting surface, that is, σ is an achronal codimension two compact surface that divides a Cauchy surface Σ into two sides, Σ in and Σ out .…”

CFT sewing as the dual of AdS cut-and-paste

“…We considered states |ψ 1 ; A , |ψ 2 ; A of fixed bulk HRT-area A that are also CPT-conjugate to each other in R, and argued that the bulk geometry dual to the sewn state |ψ 1 # R ψ 2 ; A can be obtained from the geometries g 1 (A), g 2 (A) dual to the original states |ψ 1 ; A , |ψ 2 ; A by extracting from g 1 (A), g 2 (A) the entanglement wedges of the regionsR 1 ,R 2 complementary to R and gluing these wedges together to define g(A) = g 1 (A)# R g 2 (A) as in the last line of figure 1. The work above assumed the bulk to be described by Einstein-Hilbert gravity, but using results from the forthcoming work [42] and assuming extensions of the matching conditions in [43] to the higher derivative context, analogous conclusions will continue to hold with arbitrary perturbative higher-derivative corrections.…”

“…Let us now discuss two further generalizations. First, one may note that the results of [43] allow two entanglement wedges with appropriately-compatible data on the HRTsurfaces to be directly sewn together without first embedding each in a larger geometry, and certainly without requiring the complementary wedges in that geometry to be CPTconjugate. It is thus natural to ask if there is a good CFT dual to this more general bulk gluing.…”

Areas and entropies in BFSS/gravity duality

“…We can also define an entropy associated with a more general subset of observables that does not necessarily form a subalgebra. 9 Entropies of this type have been discussed previously in the context of holography in [39][40][41]. Given a set of (not necessarily commuting) operators A = {O α } and a global state ρ, we can look for a state ρ A that maximizes the von Neumann entropy subject to the constraint that…”