^{1}

^{1}

^{3}.

We argue that certain nonviolent local quantum field theory (LQFT) modification considered at the global horizon

It has been argued in [

Following the theoretical evidence, in the current paper, we embrace the notion of locality as an effective field theory, manifesting in weak gravitational dynamics. Based on that assumption we propose a framework, featuring a modification of local quantum field theory as defined on the global horizon

By treating gravity in a black hole background metric (Minkowski space) as a field theory

The paper is organized as follows. In Section

The particular modification of LQFT, which we propose, comes from localized and brief violations of locality, yielded by “strong” fluctuations of the

Based on the thermal spectrum of the emitted radiation and black hole thermodynamics (Second Law, in particular) we now take for granted the proportionality between black hole entropy and horizon area. Namely, the entropy of a black hole is one-fourth of the area of the event horizon in Planck units:

The geometric entropy bound is deeply rooted in holography and further generalized in the Bousso bound [

We begin by showing how the Bekenstein formula can be derived from entanglement entropy and later how this can yield the small departures from LQFT needed to carry the quantum information out of the black hole.

Bianchi has shown [

Imagine we have a Schwarzschild black hole in a pure state

Here, a black hole event horizon provides a perfect entangling surface as it naturally causally disconnects the interior and exterior regions

The pure state of the complete system is given by the product of the two subsystems

The pure state of the complete system may be decomposed as

Consider the Minkowski vacuum in the region near the black hole which is bounded by a local Rindler horizon

In the vacuum state every mode on the

Bianchi’s derivation of the equality

Suppose we assign a time-dependent Killing frequency to the

We wish to focus on the black hole metric back-reaction from the

We believe that strong quantum fluctuations of the gravitational field as considered

Penrose diagram depicting the matching between the randomly embedded qubits (blue dots) and strong fluctuations (red arrows). The wave-like red line is the singularity

For convenience when describing the strong graviton fluctuations we will consider a time slice on which the mass of the hole is time-translation invariant. Hence, the influx of matter exactly matches the emission of Hawking particles to future null infinity. In the particular case the emission should be thought of as a statistical phenomena which solely depends on the internal Hilbert space _{
A}. However, small deviations may appear due to the random nature of the fluctuations (excitations). Also, consider the following assumptions: (i) the future Rindler horizon

That being said, suppose we place two corresponding strings on both sides of

(A) We think of a fluctuation of the

(B) The fluctuations below that threshold, thus

Reference [

We are interested in the quantum effects which arise when there is a correspondence in the relative states of the occupation numbers on both sides of ^{
+ }. That is a strong fluctuation in

Let us consider a portion of the Rindler-like horizon

So a strong fluctuation

We now examine the results from treating gravity as a field theory and considering the fluctuations which arise from its universal coupling to the matter fields in the vicinity of the horizon.

As it has been shown in [

Smooth behavior at

Rapidly vanishing outside

In what follows we show that the conjectured horizon fluctuations [

Let us begin with the latter constraint. The source (

The former requirement is satisfied as follows. The nonlocal effects arising from the field theory treatment of the graviton are expected to cause no drama for an observer crossing the horizon since (i) they have a lifespan of order of the fluctuation

Diagram of the near-horizon region.

In particular, let us think of the field fluctuations

Note the individual HOs need not have the same radial frequency

Note the conjectured highly localized and brief violations of locality occur only in the presence of horizon since it foliates the given space-time region into distinct causal patches with continuous transition between the corresponding CFTs; see (

Restoring the unitary evolution of a black hole in generic models requires extra quanta to be emitted. Moreover, we wish the Hawking emission deviations to be consistent with the postulates of observer complementarity, hence no divergence of the stress tensor at the horizon. Again, we focus on the coupling between graviton and matter fields in the near-horizon region

In the current Section we focus on the weak fluctuations of the graviton very near the global horizon and specifically how they can lead to the conjectured Planckian-amplitude horizon oscillations [

Let us begin by defining what we mean by weak fluctuations

The oscillations occur naturally in the process of black hole formation/evaporation and are expected in any physically meaningful theory of quantum gravity. During the evaporation of a black hole we assume

Note that

There are certain constraints that the dynamics which take care of information escape to asymptotic infinity need to respect. If we wish to keep LQFT in Minkowski space and simultaneously have spacelike transfer of quantum information a firewall will form. For that reason Giddings has argued [

Further, several authors [

By embracing the notion of locality as an effective theory and by treating gravity in Minkowski space as a field theory, we presented a scenario for adiabatic information release from a static black hole which does not cause drama for an infalling observer and begins much before Page time. Namely, by introducing extra particle radiation beyond the Hawking emission we manage to restore the unitary evolution without forming a firewall. Further, the current framework does not lead to divergence of the stress-energy tensor at the global horizon due to the early emission initiation and the low energy density of the emitted particles. The model presents perturbative quantum effects which emerge from considering strong fluctuations

The authors declare that there are no conflicts of interest regarding the publication of this paper.