Acoustic Firewalls: Analogue Gravity Perspective on the AMPS Paradox

The paper investigates whether the AMPS (Almheiri-Marolf-Polchinski-Sully) firewall paradox—which suggests that unitarity and a smooth horizon are incompatible for black holes—has a measurable analogue in sonic horizons. Specifically, the authors ask if the monogamy of entanglement forces a non-smooth state (an acoustic firewall) at the horizon of a Bose-Einstein condensate (BEC) after the analogue Page time.

The authors use the Unruh acoustic metric to model a sonic horizon in a BEC, where sound waves (phonons) behave like quantum fields in curved spacetime. They apply the AMPS argument to this system, showing that the requirement for unitary evolution after the Page time necessitates the breaking of entanglement between outgoing phonons and their interior partners. They define an 'acoustic firewall' as the resulting non-Hadamard state and calculate the expected stress-tensor signature of this state compared to a smooth, thermal horizon.

The analysis reveals that post-Page-time unitarity requires the mutual information between an outgoing phonon and its interior partner to vanish. This transition selects a Boulware-like state, which lacks the partner entanglement necessary for a smooth horizon. The authors predict a concrete, falsifiable signal: a differential phonon-calorimetry depletion ratio, R(δr) = |ΔE|/E(0) → (ℓκ/δr)^2, which grows as the inverse square of the distance from the horizon. This signal is absent before the Page time and emerges only as the system reaches its entropy limit.

This work provides a controlled, laboratory-based framework to test the kinematic consequences of the AMPS paradox. By transcribing a deep theoretical tension from quantum gravity into a measurable acoustic signal, it offers a path to experimentally probe whether horizons can maintain a smooth vacuum or if they must develop singular structures to preserve unitarity. While it does not solve the information paradox, it turns a theoretical debate into a falsifiable prediction for current BEC experiments.