Information paradox
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Understanding the Black Hole Information Paradox
Introduction to the Information Paradox
The black hole information paradox is a fundamental problem in theoretical physics that questions how information behaves in the context of black holes. Initially proposed by Stephen Hawking, the paradox arises from the apparent contradiction between quantum mechanics and general relativity. According to Hawking's calculations, black holes emit radiation (Hawking radiation) and eventually evaporate, seemingly leading to the loss of information about the matter that fell into the black hole, which contradicts the principles of quantum mechanics that assert information must be conserved 17.
Exponentially Small Correlations and Information Redundancy
Recent progress suggests that exponentially small correlations in the radiation emitted by a black hole could resolve the original paradox. These correlations imply that the information is not lost but rather encoded in subtle ways within the radiation 1. Furthermore, a principle in quantum gravity posits that a copy of all the information on a Cauchy slice is also available near the boundary of the slice. This redundancy means that the exterior of the black hole retains a complete copy of the information in the interior, providing a potential resolution to the information paradox for evaporating black holes 1.
Entanglement and Monogamy Violation
A sharp version of the information paradox involves the violation of the monogamy of entanglement during black hole evaporation. In a local quantum field theory, Bell correlations between operators in spacelike regions are monogamous. However, in a theory of gravity, this property can be violated, suggesting that what appears to be a violation of entanglement monogamy may actually be a subtle violation of locality in quantum gravity 2.
Entanglement Islands and de Sitter Holography
In de Sitter spacetime, the information paradox can be addressed through the concept of entanglement islands. These islands emerge in the context of the DS/dS correspondence, where the entanglement entropy of a subregion follows a time-dependent Page curve. This behavior suggests that the spatial distribution of microscopic degrees of freedom depends on the description, similar to black holes. In static descriptions, these degrees of freedom are localized toward the horizon, while in global descriptions, they are uniformly distributed 3.
AdS/CFT Correspondence and Operator Construction
Within the AdS/CFT correspondence, the information paradox can be reduced to the existence of certain operators in the conformal field theory (CFT). A simple construction of these operators on a given state of the CFT leads to a smooth horizon and addresses the strong subadditivity paradox while preserving locality within effective field theory. This construction reconciles the existence of the black hole interior with the growth of states with energy in the CFT 5.
Quantum Fluctuations and Horizon Disappearance
The origin of the black hole information paradox is argued to stem from treating the black hole geometry as strictly classical. Allowing the geometry to fluctuate quantum mechanically causes the horizon to effectively disappear. This implies that the information paradox is not a fundamental issue but rather a problem of describing how matter at the highest densities gravitates 6.
Fuzzball Structure and Quantum Corrections
Recent results in string theory suggest that the interior of black holes has a "fuzzball" structure, which resolves the information paradox. This nontrivial structure of microstates provides a qualitative picture of how classical intuition can break down in black hole physics. Small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole, reinforcing the need for a more profound understanding of quantum effects in black holes 78.
Conclusion
The black hole information paradox remains a profound challenge in theoretical physics, highlighting the need for a deeper understanding of the interplay between quantum mechanics and gravity. Various approaches, including exponentially small correlations, entanglement islands, and the fuzzball structure, offer promising avenues for resolving the paradox. Continued research in these areas is essential for uncovering the true nature of information in the context of black holes.
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