Diffeomorphism invariance and the black hole information paradox

Abstract

We argue that the resolution to the black hole information paradox lies in a proper accounting of the implications of diffeomorphism invariance for the Hilbert space and observables of quantum gravity. The setting of asymptotically Anti-de Sitter spacetime is adopted for most of the paper, but in the framework of canonical quantum gravity, without invoking AdS/CFT duality. We present Marolf's argument that boundary unitarity is a consequence of diffeomorphism invariance, and show that its failure to apply in the classical limit results from a lack of analyticity that has no quantum counterpart. We argue that boundary unitarity leads to a boundary information paradox, which generalizes the black hole information paradox and arises in virtually any scattering process. We propose a resolution that involves operators of the boundary algebra that redundantly encode information about physics in the bulk, and explain why such redundancy need not violate the algebraic no cloning theorem. We also argue that the infaller paradox, which has motivated the firewall hypothesis for black hole horizons, is ill-posed in quantum gravity, because it ignores essential aspects of the nature of the Hilbert space and observables in quantum gravity.

Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information

“…25 Furthermore, just as there is a particular gauge (or class of gauges) realizing ER=EPR-like scenarios, it seems likely that one can also find gauges realizing fuzzball scenarios (see e.g. [17,19,24,29,[127][128][129][130][131], the non-violent non-locality proposal 26 [20,22,30]), proposals emphasizing the bulk Wheeler-DeWitt equation [132,133], the black hole final state proposal [14], and perhaps other proposals as well.…”

Holography and unitarity

“…In order to investigate this puzzle more closely, as well as expand on the discussion of EWR, this section will begin by considering the case of "small but nonzero G D ," which we have seen is really a condition specifying a subsector of states of the R/l p 1 theory. In fact, Marolf [2][3][4] (for further discussion, see also [5,6]) has argued that holography arises from specific features unique to gravity; we can explore the validity of this proposal, beginning with the small G D limit.…”

“…In other words, locality implies that there is bulk information that is not present in any such "boundary theory." One expects to also be able to explain this by construction of a split vacuum, 6 which is a bulk state |U D 0 such that…”

“…For example, such dressings, which we write as X g (x) =x + V (x), may be explicitly constructed for metrics that are perturbations about flat space, 6) with g 0 = η (the power of κ is introduced so that h and its commutators are canonically normalized). An example is the gravitational line dressing of [29,8], which for a general curve Γ connectingx to infinity, takes the form…”

“…Gravity has been argued to play an essential role in holography [2][3][4][5][6], via gauge invariance and the gravitational constraints. This question can be examined systematically, beginning with scattering of states with weak gravitational fields, in large radius AdS.…”