Cool horizons lead to information loss

TL;DR

The work argues that preserving unitarity in black hole evaporation requires invertibility of the initial-to-final state map, which in turn forces order-one deviations from the Unruh vacuum at the horizon throughout evaporation. By demonstrating that generic black holes can be formed in arbitrary microstates (with Schwarzschild failing and D1-D5-P enabling state preparation), the paper shows that smooth horizons cannot be maintained generically, favoring fuzzball/firewall structures. It critiques mainstream proposals (e.g., Susskind-Papadodimas-Maldacena models) for not satisfying invertibility, and it connects horizon structure to thermo-field doubling and analytic continuation, while reconciling entropy counting with semi-classical gravity through AdS/CFT perspectives. The key takeaway is that the information paradox cannot be resolved by purifying the final state alone; a non-smooth, information-bearing horizon (fuzzball) appears necessary for unitary evolution of generic black holes.

Abstract

There are two evidences for information loss during black hole evaporation: (i) a pure state evolves to a mixed state and (ii) the map from the initial state to final state is non-invertible. Any proposed resolution of the information paradox must address both these issues. The firewall argument focuses only on the first and this leads to order one deviations from the Unruh vacuum for maximally entangled black holes. The nature of the argument does not extend to black holes in pure states. It was shown by Avery, Puhm and the author that requiring the initial state to final state map to be invertible mandates structure at the horizon even for pure states. The proof works if black holes can be formed in generic states and in this paper we show that this is indeed the case. We also demonstrate how models proposed by Susskind, Papadodimas et al. and Maldacena et al. end up making the initial to final state map non-invertible and thus make the horizon "cool" at the cost of unitarity.

Figures (4)

• Figure 1: Entanglement entropy of radiation from (a) a normal body in a typical state and (b) a traditional black hole with information-free horizon. In normal bodies in a typical state, the entropy initially goes up and then goes down while for traditional black holes that evaporate via Hawking-pair creation the entropy monotonically increases. Allowing small correction to the leading order process (solid line) decreases the slope (dashed line) but the entropy curve keeps rising.
• Figure 2: A black hole when placed in a perfectly reflecting container will come to equilibrium with its radiation under certain conditions. As long as such conditions are maintained, the box may be slowly expanded and contracted while keeping the total entropy of the system fixed.
• Figure 3: (a) Alice can bleach black hole and radiation system to the eternal black hole state using a powerful quantum computer. However, if this has to happen for generic states then the quantum computer has to store the state of the original system in some storage device the size of a black hole. (b) In the context of the information paradox we are more interested in what quantum gravity does than what Alice can do. If quantum gravity is to repeat Alice's task than it needs a separate storage device the size of the black hole which is bleached. In the absence of such a storage device we are back where we started -- information loss.
• Figure 4: (a) Bob who is accelerating, experiences Rindler space which is described by a thermal density matrix. Such a spacetime has a horizon. (b) Bob may use analytic continuation to assume that the full spacetime is the Minkowski vacuum. Alternately the thermo-field double of his density matrix corresponds to the Minkowski vacuum. (c) However, the actual state may have a Rindler (i.e. accelerating) elephant in the left wedge. (d) While Bob will not pay for his mistake in using analytic-continuation/TFD, Alice who listens to Bob and jumps through Bob's horizon may end up being hit by a firewall of water thrown by the elephant.