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Frozen Vacuum

Raphael Bousso

TL;DR

The paper analyzes the firewall paradox for old black holes through state-dependent interior mappings (A=R_B/ER=EPR) that would identify the interior partner with purified Hawking radiation. It shows that accommodating environmental interactions requires expanding the map to include the environment, which can freeze the near-horizon vacuum and threaten the equivalence principle. Attempts to formulate a universal rule for when to apply the interior map fail in the presence of large, scrambled radiation and even with quantum-error-correction intuition, as the purification becomes global. The work highlights a fundamental tension between interior reconstruction, environmental decoherence, and the equivalence principle, with significant implications for black hole information and quantum gravity.

Abstract

Modes just outside the horizon of a typical old black hole are thermally entangled with distant Hawking radiation. This precludes their entangled purity with interior modes, leading to a firewall. Identifying the interior with the distant radiation ("A=R_B", "ER=EPR") can resolve the entanglement conflict. But the map must adjust for any interactions, or else the firewall will reappear if the Hawking radiation scatters off the CMB. With a self-correcting map, an infalling observer is unable to excite the vacuum near the horizon. This allows the horizon to be locally detected and so violates the equivalence principle.

Frozen Vacuum

TL;DR

The paper analyzes the firewall paradox for old black holes through state-dependent interior mappings (A=R_B/ER=EPR) that would identify the interior partner with purified Hawking radiation. It shows that accommodating environmental interactions requires expanding the map to include the environment, which can freeze the near-horizon vacuum and threaten the equivalence principle. Attempts to formulate a universal rule for when to apply the interior map fail in the presence of large, scrambled radiation and even with quantum-error-correction intuition, as the purification becomes global. The work highlights a fundamental tension between interior reconstruction, environmental decoherence, and the equivalence principle, with significant implications for black hole information and quantum gravity.

Abstract

Modes just outside the horizon of a typical old black hole are thermally entangled with distant Hawking radiation. This precludes their entangled purity with interior modes, leading to a firewall. Identifying the interior with the distant radiation ("A=R_B", "ER=EPR") can resolve the entanglement conflict. But the map must adjust for any interactions, or else the firewall will reappear if the Hawking radiation scatters off the CMB. With a self-correcting map, an infalling observer is unable to excite the vacuum near the horizon. This allows the horizon to be locally detected and so violates the equivalence principle.

Paper Structure

This paper contains 6 sections, 11 equations, 1 figure.

Table of Contents

  1. Spread purification
  2. Frozen vacuum
  3. A more complicated rule?
  4. Large systems
  5. Quantum error correction
  6. Acknowledgments

Figures (1)

  • Figure 1: A pointer interacts with an outgoing wavepacket in the zone. The equivalence principle then demands that Alice must not find the vacuum at the horizon. But the same exterior state will result if the pointer instead measures the purification of $b$ in the Hawking radiation (not shown). A self-correcting construction of the interior mode $\tilde{b}$ cannot distinguish between these two processes, and so will produce the vacuum in both cases. Without corrections for interactions, the map will produce a firewall even if only the Hawking radiation interacts. Either way, the horizon is special.