Proof of a New Area Law in General Relativity

A future holographic screen is a hypersurface of indefinite signature, foliated by marginally trapped surfaces with area $A(r)$. We prove that $A(r)$ grows strictly monotonically. Future holographic screens arise in gravitational collapse. Past holographic screens exist in our own universe; they obey an analogous area law. Both exist more broadly than event horizons or dynamical horizons. Working within classical General Relativity, we assume the null curvature condition and certain generiticity conditions. We establish several nontrivial intermediate results. If a surface $\sigma$ divides a Cauchy surface into two disjoint regions, then a null hypersurface $N$ that contains $\sigma$ splits the entire spacetime into two disjoint portions: the future-and-interior, $K^+$; and the past-and-exterior, $K^-$. If a family of surfaces $\sigma(r)$ foliate a hypersurface, while flowing everywhere to the past or exterior, then the future-and-interior $K^+(r)$ grows monotonically under inclusion. If the surfaces $\sigma(r)$ are marginally trapped, we prove that the evolution must be everywhere to the past or exterior, and the area theorem follows. A thermodynamic interpretation as a Second Law is suggested by the Bousso bound, which relates $A(r)$ to the entropy on the null slices $N(r)$ foliating the spacetime. In a companion letter, we summarize the proof and discuss further implications.Comment: 15 pages, 10 figures; v4: conclusion of Theorem IV.2 strengthene

Locality from Quantum Gravity: All or Nothing

In a full theory of quantum gravity, local physics is expected to be approximate rather than innate. It is therefore important to understand how approximate locality emerges in the semiclassical limit. Here we show that any notion of locality emergent from a holographic theory of quantum gravity is "all or nothing": local data is not obtained gradually from subregions of the boundary, but is rather obtained all at once when enough of the boundary is accessed. Our assumptions are mild and thus this feature is quite general; in the special case of AdS/CFT, a slightly different manifestation follows from well-known and familiar properties.Comment: 7 pages; 4 figures. v2: added references, minor edit

A New Area Law in General Relativity

We report a new area law in General Relativity. A future holographic screen is a hypersurface foliated by marginally trapped surfaces. We show that their area increases monotonically along the foliation. Future holographic screens can easily be found in collapsing stars and near a big crunch. Past holographic screens exist in any expanding universe and obey a similar theorem, yielding the first rigorous area law in big bang cosmology. Unlike event horizons, these objects can be identified at finite time and without reference to an asymptotic boundary. The Bousso bound is not used, but it naturally suggests a thermodynamic interpretation of our result.Comment: 4 pages, 2 figures; v3: typos fixe

Evidence for Dynamic Excitation-Inhibition Ratio in Networks of Cortical Neurons

In this report trial-to-trial variations in the synchronized responses of neural networks are offered as evidence for excitation-inhibition ratio being a dynamic variable over time scales of minutes. Synchronized network responses to stimuli were studied in ex-vivo large scale cortical networks. We show that sub-second measures of the individual synchronous response, namely -- its latency and decay duration, are related to minutes-scale network response dynamics. Network responsiveness is reflected as residency in, or shifting amongst, areas of the latency-decay plane. The different sensitivities of latency and decay durations to synaptic blockers imply that these two measures reflect the effective impacts of inhibitory and excitatory neuronal populations on response dynamics. Taken together, the data suggest that network response variations under repeated stimuli result from excitation-inhibition ratio being a dynamic variable rather than a parameter

Generalized Second Law for Cosmology

We conjecture a novel Generalized Second Law that can be applied in cosmology, regardless of whether an event horizon is present: the generalized entropy increases monotonically outside of certain hypersurfaces we call past Q-screens. A past Q-screen is foliated by surfaces whose generalized entropy (sum of area and entanglement entropy) is stationary along one future null direction and increasing along the other. We prove that our Generalized Second Law holds in spacetimes obeying the Quantum Focussing Conjecture. An analogous law applies to future Q-screens, which appear inside evaporating black holes and in collapsing regions.Comment: 14 pages, 5 figure

Causal Density Matrices

We define a new construct in quantum field theory - the causal density matrix - obtained from the singularity structure of correlators of local operators. This object provides a necessary and sufficient condition for a quantum field theory state to have a holographic semiclassical dual causal geometry. By exploiting the causal density matrix, we find that these dual causal geometries quite generally (even away from AdS/CFT) exhibit features of quantum error correction. Within AdS/CFT, we argue that the "reduced" causal density matrix is the natural dual to the causal wedge. Our formalism is very well-suited to generalizations of holography beyond AdS/CFT or even gravity/QFT.Comment: 34+4 pages, 10 figures. v2: minor edits, references added. v3: minor typos correcte

Covariant Constraints on Hole-ography

Hole-ography is a prescription relating the areas of surfaces in an AdS bulk to the differential entropy of a family of intervals in the dual CFT. In (2+1) bulk dimensions, or in higher dimensions when the bulk features a sufficient degree of symmetry, we prove that there are surfaces in the bulk that cannot be completely reconstructed using known hole-ographic approaches, even if extremal surfaces reach them. Such surfaces lie in easily identifiable regions: the interiors of holographic screens. These screens admit a holographic interpretation in terms of the Bousso bound. We speculate that this incompleteness of the reconstruction is a form of coarse-graining, with the missing information associated to the holographic screen. We comment on perturbative quantum extensions of our classical results.Comment: 26+4 pages, 16 figures; v2: references added, typos fixe

The Gravity Dual of Boundary Causality

In gauge/gravity duality, points which are not causally related on the boundary cannot be causally related through the bulk; this is the statement of boundary causality. By the Gao-Wald theorem, the averaged null energy condition in the bulk is sufficient to ensure this property. Here we proceed in the converse direction: we derive a necessary as well as sufficient condition for the preservation of boundary causality under perturbative (quantum or stringy) corrections to the bulk. The condition that we find is a (background-dependent) constraint on the amount by which light cones can "open" over all null bulk geodesics. We show that this constraint is weaker than the averaged null energy condition.Comment: 14+5 pages, 3 figures. v2: addressed referee comments; amended figure

Surface Theory: the Classical, the Quantum, and the Holographic

Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we consider modifications to their boundary conditions, to the bulk metric, and to bulk quantum matter fields. We present a unified framework for treating such perturbations for classical extremal surfaces, classify some of their stability properties, and develop new technology to extend our treatment to quantum extremal surfaces, culminating in an "equation of quantum extremal deviation". The power of this formalism stems from its ability to map geometric statements into the language of elliptic operators; to illustrate, we show that various a priori disparate bulk constraints all follow from basic consistency of subregion/subregion duality. These include familiar properties such as (smeared) versions of the quantum focusing conjecture and the generalized second law, as well as new constraints on (i) metric and matter perturbations in spacetimes close to vacuum and (ii) the bulk stress tensor in generic (not necessary close to vacuum) spacetimes. This latter constraint is highly reminiscent of a quantum energy inequality.Comment: 75 (60+9+6) pages, 13 figures. v2: fixed typos, minor clarification

Inhibition in Random Neuronal Networks Enhances Response Variability and Disrupts Stimulus Discrimination

Inhibition is considered to shape neural activity, and broaden its pattern repertoire. In the sensory organs, where the anatomy of neural circuits is highly structured, lateral inhibition sharpens contrast among stimulus properties. The impact of inhibition on stimulus processing and the involvement of lateral inhibition is less clear when activity propagates to the less-structured relay stations. Here we take a synthetic approach to disentangle the impacts of inhibition from that of specialized anatomy on the repertoire of evoked activity patterns, and as a result, the network capacity to uniquely represent different stimuli. To this aim, we blocked inhibition in randomly rewired networks of cortical neurons in-vitro, and quantified response variability and stimulus discrimination among stimuli provided at different spatial loci, before and after the blockade. We show that blocking inhibition quenches variability of responses evoked by repeated stimuli through any spatial source; for all tested response features. Despite the sharpening role of inhibition in the highly structured sensory organs, in these random networks we find that blocking inhibition enhances stimulus discrimination between spatial sources of stimulation, when based on response features that emphasize the relation among spike times recorded through different electrodes. We further show that under intact inhibition, responses to a given stimulus are a noisy version of those revealed by blocking inhibition; such that intact inhibition disrupts an otherwise coherent, wave propagation of activity