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arXiv:hep-th/0403268 · Fortschritte der Physik

On long time unitarity restoring processes in the presence of eternal black holes

J.L.F. Barbón, E. Rabinovici

Published May 13, 2004• 48 citations
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Abstract

Abstract We discuss the various scales determining the temporal behaviour of correlation functions in the presence of eternal black holes. We point out the origins of the failure of the semiclassical gravity approximation to respect a unitarity‐based bound suggested by Maldacena. We find that the presence of a subleading (in the large N approximation involved) master field does restore the compliance with one bound but additional configurations are needed to explain the more detailed expected time dependence of the Poincare recurrences and their magnitude.

DOI
10.1002/prop.200410157

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Abstract We discuss the various scales determining the temporal behaviour of correlation functions in the presence of eternal black holes. We point out the origins of the failure of the semiclassical gravity approximation to respect a unitarity‐based bound suggested by Maldacena. We find that the presence of a subleading (in the large N approximation involved) master field does restore the compliance with one bound but additional configurations are needed to explain the more detailed expected time dependence of the Poincare recurrences and their magnitude.
We discuss the various scales determining the temporal behaviour of correlation functions in the presence of eternal black holes.We point out the origins of the failure of the semiclassical gravity approximation to respect a unitarity-based bound suggested by Maldacena.We find that the presence of a subleading (in the large N approximation involved) master field does restore the compliance with one bound but additional configurations are needed to explain the more detailed expected time dependence of the Poincare recurrences and their magnitude.
Recent works suggest that quantum theory may support a unification of the notions of space and time, thus treating the spatial and temporal quantum correlations equally. Specifically, the partial transposition of the maximally entangled state of two quantum systems at one time exactly matches the temporal quantum correlations of one quantum system that evolves unitary between two distinct moments of time. In this work we consider this equivalence of spatial and temporal quantum correlations in the context of AdS/CFT duality. We show that in the high temperature limit the thermofield double state is equivalent to the temporal quantum correlations of a quantum theory evolving unitary between two times. Thus, on the gravity side, we argue that the temporal correlations correspond to a black hole at one time connected behind the horizon by an Einstein-Rosen bridge to the same black hole at another time. Moreover, we construct the spacetime corresponding to this temporal wormholes and find that the spacetime is consistent with the interior solution of the BTZ black hole. We conclude suggesting that the BTZ interior solution could have an interpretation in the dS/CFT correspondence framework.
An important question about black holes is to what extent a typical pure state differs from the ensemble average. We show that this question can be answered within semi-classical gravity. We focus on the quantum deviation, which measures the fluctuations in the expectation value of an operator in an ensemble of pure states. For a large class of ensembles and observables, these fluctuations are calculated by a correlation function in the eternal black hole background, which can be reliably calculated within semi-classical gravity. This implements the idea of [arXiv:2002.02971] that wormholes can arise from averages over states rather than theories. As an application, we calculate the size of the long-time correlation function \langle A(t) A(0)\rangle ⟨ A ( t ) A ( 0 ) ⟩ .
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational dynamics with respect to this coherent state basis, which generates time evolution of the spacetime with respect to a clock at infinity. Since the coherent states are not orthogonal, an initial quasiclassical geometry is dynamically driven into a superposition of different amplitudes. Our framework provides a dynamical mechanism for tunneling between geometries that is ubiquitous in a number of approaches to quantum gravity, from loop quantum gravity to the Euclidean path integral. We apply our framework to the problem of black hole evaporation, providing a hint at how unitarity may be preserved with the inclusion of quantum corrections to the semiclassical evolution of the black hole.
We discuss the black hole information problem, including the recent claim that unitarity requires a horizon firewall, emphasizing the role of decoherence and macroscopic superpositions. We consider the formation and evaporation of a large black hole as a quantum amplitude, and note that during intermediate stages (e.g., after the Page time), the amplitude is a superposition of macroscopically distinct (and decohered) spacetimes, with the black hole itself in different positions on different branches. Small but semiclassical observers (who are themselves part of the quantum amplitude) that fall into the hole on one branch will miss it entirely on other branches and instead reach future infinity. This observation can reconcile the subjective experience of an infalling observer with unitarity. We also discuss implications for the nice slice formulation of the information problem, and to complementarity.
It has recently been suggested that black holes may be described as condensates of weakly interacting gravitons at a critical point, exhibiting strong quantum effects. In this paper, we study a model system of attractive bosons in one spatial dimension which is known to undergo a quantum phase transition. We demonstrate explicitly that indeed quantum effects are important at the critical point, even if the number of particles is macroscopic. Most prominently, we evaluate the entropy of entanglement between different momentum modes and observe it to become maximal at the critical point. Furthermore, we explicitly see that the leading entanglement is between long-wavelength modes and is hence a feature independent of ultraviolet physics. If applicable to black holes, our findings substantiate the conjectured breakdown of semiclassical physics even for large black holes. This can resolve long-standing mysteries, such as the information paradox and the no-hair theorem.