Black holes, information, and Hilbert space for quantum gravity

Abstract

A coarse-grained description for the formation and evaporation of a black hole is given within the framework of a unitary theory of quantum gravity preserving locality, without dropping the information that manifests as macroscopic properties of the state at late times. The resulting picture depends strongly on the reference frame one chooses to describe the process. In one description based on a reference frame in which the reference point stays outside the black hole horizon for sufficiently long time, a late black hole state becomes a superposition of black holes in different locations and with different spins, even if the back hole is formed from collapsing matter that had a well-defined classical configuration with no angular momentum. The information about the initial state is partly encoded in relative coefficientsespecially phases-of the terms representing macroscopically different geometries. In another description in which the reference point enters into the black hole horizon at late times, an S-matrix description in the asymptotically Minkowski spacetime is not applicable, but it sill allows for an "S-matrix" description in the full quantum gravitational Hilbert space including singularity states. Relations between different descriptions are given by unitary transformations acting on the full Hilbert space, and they in general involve superpositions of "distant" and "infalling" descriptions. Despite the intrinsically quantum mechanical nature of the black hole state, measurements performed by a classical physical observer are consistent with those implied by general relativity. In particular, the recently-considered firewall phenomenon can occur only for an exponentially fine-tuned (and intrinsically quantum mechanical) initial state, analogous to an entropy decreasing process in a system with large degrees of freedom.

An infalling observer in AdS/CFT

“…We expect that this is only a tree-level coincidence and cannot be extended to higher orders in 1 N . 19 Although, for notational reasons, we presented the results for a black brane it should be clear that similar local bulk observables can be defined for a big black hole in global AdS, by replacing the integrals over k with sums over spherical harmonics.…”

“…If we write the bulk field as 19) then merely the fact that φ CFT must satisfy the canonical commutation relations near the horizon tells us that we must have…”

“…Even though the principle of equivalence suggests that there is nothing special about the horizon of a large black hole, there have been several speculations that quantum gravity effects cause the interior to be modified into a fuzzball [1][2][3][4][5], and more recently, that the horizon of an "old black hole" is replaced by a firewall [6]. (See also [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].) These latter proposals originate, not from direct calculations in quantum gravity, but rather in arguments that the information paradox (in various incarnations) cannot be solved without modifying the geometry at, or behind the horizon.…”

Phases of information release during black hole evaporation

“…Recently, a modern interpretation of the information-loss paradox, known as the "firewall" problem [25] (also see [9-11, 26, 27] for earlier versions and [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] for a sample of the related literature). We find the current analysis to be an essential step toward a resolution of this puzzle, but defer this discussion to future publications [46,47].…”

Hyper-entropic gravitational fireballs (grireballs) with firewalls

“…* Internet address: profdonpage@gmail.com 1 Recently Almheiri, Marolf, Polchinski, and Sully [1] have given a provocative argument that suggests that an "infalling observer burns up at the horizon" of a sufficiently old black hole, so that the horizon becomes what they called a "firewall. "This paper has elicited a large number of responses, some of which support the firewall idea [2,3,4,5], others of which raise skepticism about it [6,7,8,9,10,11,12,13,14,15,16], and yet others seem more agnostic [17,18].(Samuel Braunstein has informed me that he and Pirandola andŻyczkowski had written a paper [19] that had earlier derived the identical phenomenon which they called "energetic curtains," but that paper makes rather different assumptions and comes to the conclusion that "the information entering a black hole . .…”