The Information Paradox for Black Holes (1509.01147v1)

Abstract: I propose that the information loss paradox can be resolved by considering the supertranslation of the horizon caused by the ingoing particles. Information can be recovered in principle, but it is lost for all practical purposes.

• The paper proposes resolving the black hole information paradox by showing information is encoded on the horizon via supertranslations.
• Information from ingoing particles is encoded onto the event horizon via induced supertranslations, preserving it and influencing the pattern of outgoing radiation.
• This symmetry-based approach using supertranslations resolves the paradox and preserves unitarity, though the encoded information is practically inaccessible.

Resolving the Black Hole Information Paradox Through Horizon Supertranslations

The paper "The Information Paradox for Black Holes" by S.W. Hawking addresses a long-standing problem in theoretical physics concerning the fate of information in black hole evaporation. Since Hawking's seminal work four decades ago, the information paradox has challenged the understanding of quantum mechanics and general relativity integration. This paper proposes a novel conceptual approach to the paradox, which reconciles the apparent information loss in black holes with the unitarity of the S-matrix by introducing the influence of supertranslations on the event horizon.

Hawking's initial assertion was that black hole evaporation leads to a loss of information, resulting in outgoing radiation being in a mixed state, thereby implying a non-unitary S-matrix. This view has been contested due to developments such as the AdS/CFT correspondence, which postulates no loss of information. Consequently, the core paradox is how information about the quantum state of infalling particles can emerge with the outgoing radiation. This paper presents a solution by positing that information is encoded not within the black hole's interior but on its boundary, specifically the event horizon, aligning with holographic principles.

The paper capitalizes on supertranslations, originally introduced in 1962 to depict asymptotic symmetries in flat spacetime with gravitational radiation. The BMS group, describing such symmetries, illustrates how supertranslations shift retarded time along the null generators of infinity. Having attended a lecture by Strominger on this topic, Hawking draws parallels between supertranslations on I+ and those affecting stationary black hole horizons. For black holes, the advanced time is shifted along the horizon's null geodesic generators, providing a mechanism by which ingoing particles induce supertranslations.

These supertranslations effectively act as a hologram, carrying information about the ingoing particles. The imprint left by supertranslations manifests in the outgoing particles in a deterministic yet chaotic fashion, suggesting no intrinsic loss of information. However, practical constraints render this information inaccessible in any utilitarian form. This proposition implies that incoming particles perturb the horizon in such a way that leads to varied emission delays of outgoing wave packets—though highly scrambled, the information is in principle preserved.

Hawking differentiates his approach from previous theories by emphasizing that his resolution is rooted in the symmetry properties of supertranslations rather than relying on high-energy corrections near the horizon. The claim that supertranslations ensure unitarity of the black hole S-matrix offers an elegant symmetry-based resolution to the paradox. The implications of this work extend to theories involving black holes in various cosmological backgrounds, potentially affirming the universality of this approach.

In conclusion, while the theoretical resolution of the black hole information paradox via horizon supertranslations is compelling, the paper acknowledges that the information—although not lost—is practically irretrievable. It suggests a framework grounded in symmetry considerations that might prompt further research into the nature of information encoding and retrieval in black holes. Collaborative explorations with M.J. Perry and A. Strominger, as mentioned, signal continued advancements in this domain, paving the way for experimental validations and theoretical refinements in resolving one of the most profound paradoxes in theoretical physics.