[Paper Review] The Transfer of Entanglement: The Case for Firewalls

Leonard Susskind|arXiv (Cornell University)|Oct 7, 2012

Black Holes and Theoretical PhysicsPhysics and Astronomy25 references73 citations

TL;DR

This paper argues that as a black hole evaporates, entanglement between its near-horizon degrees of freedom and its interior is gradually transferred to the Hawking radiation. At the Page time, when half the black hole's entropy has been radiated, this transfer completes, leading to the breakdown of the smooth horizon and the formation of a firewall, a consequence of the failure to reconstruct interior degrees of freedom without violating quantum monogamy.

ABSTRACT

Black hole complementarity requires that the interior of a black hole be represented by the same degrees of freedom that describe its exterior. Entanglement plays a crucial role in the reconstruction of the interior degrees of freedom. This connection is manifest in "two-sided" eternal black holes. But for real black holes which are formed from collapse there are no second sides. The sense in which horizon entropy is entanglement entropy is much more subtle for one-sided black holes. It involves entanglement between different parts of the near-horizon system. As a one-sided black hole evaporates the entanglement that accounts for its interior degrees of freedom disappears, and is gradually replaced by entanglement with the outgoing Hawking radiation. A principle of "transfer of entanglement" can be formulated. According to the argument of Almheiri, Marolf, Polchinski and Sully, it is when the transfer of entanglement is completed at the Page time, that a firewall replaces the horizon. Alternatives to firewalls may suffer contradictions which are similar to those of time travel. The firewall hypothesis would be similar to Hawking's chronology protection conjecture.

Motivation & Objective

• To clarify how entanglement between near-horizon and interior degrees of freedom underpins black hole complementarity in one-sided black holes.
• To analyze the evolution of entanglement during black hole evaporation, particularly the shift from horizon-based to radiation-based entanglement.
• To argue that the completion of this entanglement transfer at the Page time necessitates a firewall, preventing information loss and unitarity violation.
• To evaluate alternatives to firewalls, especially the idea of reconstructing interior physics from distant Hawking radiation, and show their potential for logical contradictions resembling time travel.

Proposed method

• Uses a model of black hole degrees of freedom: a thermal atmosphere above the horizon and a stretched horizon of fast-scrambling qubits.
• Applies the pull-back—push-forward procedure to reconstruct interior operators from exterior degrees of freedom, showing its breakdown after scrambling time.
• Quantifies entanglement degradation via mutual information and distillable entanglement, showing it diminishes to zero at the Page time.
• Analyzes the implications of replacing near-horizon entanglement (B′) with entanglement in early Hawking radiation (RB) for interior reconstruction.
• Considers the logical consistency of such a reconstruction, highlighting risks of closed timelike curves if information is retrieved and reinserted.
• Draws analogy to Hawking’s chronology protection conjecture, suggesting firewalls may serve a similar role in preserving causal structure.

Experimental results

Research questions

• RQ1 How does entanglement between near-horizon and interior degrees of freedom evolve during black hole evaporation?
• RQ2 What happens to the interior geometry when near-horizon entanglement is fully transferred to Hawking radiation?
• RQ3 Can the interior of a black hole be reconstructed from Hawking radiation alone after the Page time without violating quantum monogamy?
• RQ4 What are the logical consequences of attempting to retrieve and reinsert information from early Hawking radiation into the black hole?
• RQ5 Why might a firewall form precisely at the Page time, and how does this resolve the black hole information paradox?

Key findings

• Entanglement between the black hole’s near-horizon region and its interior degrades over time, with distillable entanglement vanishing at the Page time.
• The mutual information between the horizon and interior regions drops to zero at the Page time, signaling the end of the ability to reconstruct the interior via near-horizon degrees of freedom.
• Firewalls emerge as a necessary consequence of the breakdown of near-horizon entanglement, preventing the violation of quantum monogamy and unitarity.
• Alternative reconstruction using early Hawking radiation leads to paradoxes resembling time travel, suggesting such schemes are physically inconsistent.
• The firewall acts as a chronology protection mechanism, analogous to Hawking’s conjecture, preventing closed timelike curves in quantum gravity.
• The interior geometry is not classically describable after the Page time; its degradation may be non-classical and non-local, beyond standard spacetime geometry.