Black hole complementarity

Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by Leonard Susskind, Larus Thorlacius, and Gerard 't Hooft.

Overview
Ever since Stephen Hawking suggested information is lost in an evaporating black hole once it passes through the event horizon and is inevitably destroyed at the singularity, and that this can turn pure quantum states into mixed states, some physicists have wondered if a complete theory of quantum gravity might be able to conserve information with a unitary time evolution. But how can this be possible if information cannot escape the event horizon without traveling faster than light? This seems to rule out Hawking radiation as the carrier of the missing information. It also appears as if information cannot be "reflected" at the event horizon as there is nothing special about the horizon locally.

Leonard Susskind proposed a radical resolution to this problem by claiming that the information is both reflected at the event horizon and passes through the event horizon and cannot escape, with the catch being no observer can confirm both stories simultaneously. According to an external observer, the infinite time dilation at the horizon itself makes it appear as if it takes an infinite amount of time to reach the horizon. He also postulated a stretched horizon, which is a membrane hovering about a Planck length outside the event horizon and which is both physical and hot. According to the external observer, infalling information heats up the stretched horizon, which then reradiates it as Hawking radiation, with the entire evolution being unitary. However, according to an infalling observer, nothing special happens at the event horizon itself, and both the observer and the information will hit the singularity. This isn't to say there are two copies of the information lying about — one at or just outside the horizon, and the other inside the black hole — as that would violate the no-cloning theorem. Instead, an observer can only detect the information at the horizon itself, or inside, but never both simultaneously. Complementarity is a feature of the quantum mechanics of noncommuting observables, and Susskind proposed that both stories are complementary in the quantum sense, that there is no contradiction which also means no violation of linearity in quantum mechanics.

An infalling observer will see the point of entry of the information as being localized on the event horizon, while an external observer will notice the information being spread out uniformly over the entire stretched horizon before being re-radiated, and perceives the event horizon as a dynamical membrane. To an infalling observer, information and entropy pass through the horizon with nothing of interest happening. To an external observer, the information and entropy is absorbed into the stretched horizon which acts like a dissipative fluid with entropy, viscosity and electrical conductivity. See the membrane paradigm for more details. The stretched horizon is conducting with surface charges which rapidly spread out logarithmically over the horizon.

It has been suggested that black hole complementarity combined with the monogamy of entanglement implies the existence of an AMPS "firewall", where high energy, short wavelength photons are present in the horizon, although this hypothesis is still being developed.

A quantitative formulation
To understand the origin of Bekenstein-Hawking entropy, reference proposes a quantitative formulation of black hole complementarity, which states that both the outside fixed position observer and the inside co-moving observer's description of the microscopic state of black holes are equally right and complete. However, hybridising the two will cause errors. In physical black holes, i.e., those forming through gravitational collapse, outside fixed position observers will see matter cores continuously collapsing but never contracting smaller than the horizon size and causing singularity in the central point because the domain of time they use does not cover the range of such events' occurrence. Meanwhile, inside co-moving observers will see periodically oscillating matter cores because the equivalence principle implies that the collapse of matter across the horizon and over-cross the instantaneously singular central point is equally easy and trivial.

A statistical or ensemble description for the outside fixed position observers becomes necessary if they give up information about the initial state of the collapsing stars, believing that the collapse will lead to a final geometry with a fully realized horizon. The ergodicity of the inside co-moving observers' oscillations around the system's center becomes unavoidable due to the complexity of interactions between different parts of the collapsing star. The initial state ensemble of the outside fixed position observers and the ergodic oscillations of the inside co-moving observers form a quantitative complementarity for the microscopic state of physical black holes. References and demonstrate that quantizing either of these two descriptions yields the correct area law formulas for the Bekenstein-Hawking entropy.

According to this complementarity, the microscopic state of black holes with apriori singularity such as those described by the Schwarzschild metric will be unique and they will not experience Hawking radiation because infinitely long time is needed for any particles resulting from the vacuum pair production to fall across the horizon and hit annihilation partners inside it. However, for black holes with inner structures endowed by this complementarity, matter is distributed in a region slightly larger than the horizon size, rather than accumulating on a central point. So particles falling towards the horizon will find annihilation partners as they get to the horizon close enough. The requirement that the ingoing partners of all truly detected outgoing Hawking particles annihilate with particles inside the matter region within the time allowed by the uncertainty principle will couple Hawking particles with the change of microscopic state of black holes. This implies that hawking radiation happens through mechanisms of gravity-induced spontaneous radiation or other similars.