Is the firewall consistent?: Gedanken experiments on black hole complementarity and firewall proposal

TL;DR

The paper critically examines black hole complementarity and the firewall proposal, arguing that original complementarity is inconsistent under large $N$ rescaling and AMPS-type arguments. It introduces a gravitational-collapse toy model with a false vacuum lump to realize disconnected apparent horizons and to test whether a firewall can consistently resolve duplication without affecting future infinity. Numerical simulations reveal that a firewall near the time-like apparent horizon, in scenarios with disconnected horizons, would necessarily influence the asymptotic region, effectively making it observable at infinity. The authors conclude that maintaining complementarity requires additional assumptions, or substantial modifications to semi-classical gravity or the entropy-area relation, highlighting the need for further theoretical development in firewall physics and black hole information. This work thus links horizon structure, quantum information, and macroscopic gravitational effects to guide ongoing debates about black hole information preservation and firewall viability.

Abstract

In this paper, we discuss the black hole complementarity and the firewall proposal at length. Black hole complementarity is inevitable if we assume the following five things: unitarity, entropy-area formula, existence of an information observer, semi-classical quantum field theory for an asymptotic observer, and the general relativity for an in-falling observer. However, large N rescaling and the AMPS argument show that black hole complementarity is inconsistent. To salvage the basic philosophy of the black hole complementarity, AMPS introduced a firewall around the horizon. According to large N rescaling, the firewall should be located close to the apparent horizon. We investigate the consistency of the firewall with the two critical conditions: the firewall should be near the time-like apparent horizon and it should not affect the future infinity. Concerning this, we have introduced a gravitational collapse with a false vacuum lump which can generate a spacetime structure with disconnected apparent horizons. This reveals a situation that there is a firewall outside of the event horizon, while the apparent horizon is absent. Therefore, the firewall, if it exists, not only does modify the general relativity for an in-falling observer, but also modify the semi-classical quantum field theory for an asymptotic observer.

Figures (12)

• Figure 1: Emission of information, where $f$ is the ratio of the escaped coarse-grained entropy to the original coarse-grained entropy.
• Figure 2: The duplication experiment. $a$ and $b$ are a pair of correlated spins. The observer sees $h$ which is a copy of $a$, after the information retention time via Hawking radiation. $a$ should be sent to the out-going direction after the time $\Delta t$ in order to be observed. If the observer sees both $a$ and $h$, since they are both correlated to $b$, it violates the no-cloning theorem and unitarity.
• Figure 3: The duplication experiment conducted outside the event horizon. $a$ is in-going information and a signal is being sent to the out-going direction. This can be both inside and outside of the event horizon. To see $a$ inside the event horizon, $a$ should be sent to an out-going direction after time $\Delta t$, while to see it outside the event horizon, $a$ should be sent after time $\Delta U$.
• Figure 4: Left: The signal from the firewall (thick red arrow) kills the in-falling information. However, it does not affect outside as the effects (red dotted arrow) is screened by the apparent horizon. Right: If the apparent horizon is disconnected, then there is no screen such that the effects (red dotted arrow) can modify the asymptotic infinity.
• Figure 5: General global structure of a gravitational collapse in the presence of a false vacuum bubble. Here, $\Delta=0.07$. Color denotes the field value $S$ and red curves denote the apparent horizons.