2014 信息保留与黑洞的天气预报-精品文档资料整理.pdf

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1、Information Preservation and Weather Forecasting for BlackHolesS. W. Hawking11DAMTP, University of Cambridge, UKAbstractIt has been suggested 1 that the resolution of the information paradox for evaporating blackholes is that the holes are surrounded by firewalls, bolts of outgoing radiation that wo

2、uld destroyany infalling observer. Such firewalls would break the CPT invariance of quantum gravity and seemto be ruled out on other grounds. A different resolution of the paradox is proposed, namely thatgravitational collapse produces apparent horizons but no event horizons behind which information

3、 islost. This proposal is supported by ADS-CFT and is the only resolution of the paradox compatiblewith CPT. The collapse to form a black hole will in general be chaotic and the dual CFT on theboundary of ADS will be turbulent. Thus, like weather forecasting on Earth, information willeffectively be

4、lost, although there would be no loss of unitarity.Talk given at the fuzz or fire workshop, The Kavli Institute for Theoretical Physics, Santa Barbara, August20131arXiv:1401.5761v1 hep-th 22 Jan 2014Some time ago 2 I wrote a paper that started a controversy that has lasted until thepresent day. In t

5、he paper I pointed out that if there were an event horizon, the outgoingstate would be mixed. If the black hole evaporated completely without leaving a remnant,as most people believe and would be required by CPT, one would have a transition froman initial pure state to a mixed final state and a loss

6、 of unitarity. On the other hand, theADS-CFT correspondence indicates that the 7evaporating black hole is dual to a unitaryconformal field theory on the boundary of ADS. This is the information paradox.Recently there has been renewed interest in the information paradox 1. The authorsof 1 suggested t

7、hat the most conservative resolution of the information paradox would bethat an infalling observer would encounter a firewall of outgoing radiation at the horizon.There are several objections to the firewall proposal. First, if the firewall were locatedat the event horizon, the position of the event

8、 horizon is not locally determined but is afunction of the future of the spacetime.Another objection is that calculations of the regularized energy momentum tensor ofmatter fields are regular on the extended Schwarzschild background in the Hartle-Hawkingstate 3, 4.The outgoing radiating Unruh state

9、differs from the Hartle-Hawking statein that it has no incoming radiation at infinity. To get the energy momentum tensor inthe Unruh state one therefore has to subtract the energy momentum tensor of the ingoingradiation from the energy momentum in the Hartle-Hawking state. The energy momentumtensor

10、of the ingoing radiation is singular on the past horizon but is regular on the futurehorizon. Thus the energy momentum tensor is regular on the horizon in the Unruh state.So no firewalls.For a third objection to firewalls I shall assume that if firewalls form around black holesin asymptotically flat

11、 space, then they should also form around black holes in asymptoticallyanti deSitter space for very small lambda. One would expect that quantum gravity shouldbe CPT invariant. Consider a gedanken experiment in which Lorentzian asymptotically antideSitter space has matter fields excited in certain mo

12、des. This is like the old discussionsof a black hole in a box 5. Non-linearities in the coupled matter and gravitational fieldequations will lead to the formation of a black hole 6. If the mass of the asymptotically antideSitter space is above the Hawking-Page mass 7, a black hole with radiation wil

13、l be themost common configuration. If the space is below that mass the most likely configurationis pure radiation.2Whether or not the mass of the anti deSitter space is above the Hawking-Page massthe space will occasionally change to the other configuration, that is the black hole abovethe Hawking-P

14、age mass will occasionally evaporate to pure radiation, or pure radiation willcondense into a black hole. By CPT the time reverse will be the CP conjugate. This showsthat, in this situation, the evaporation of a black hole is the time reverse of its formation(modulo CP), though the conventional desc

15、riptions are very different. Thus if one assumequantum gravity is CPT invariant, one rules out remnants, event horizons, and firewalls.Further evidence against firewalls comes from considering asymptotically anti deSitter tothe metrics that fit in an S1 cross S2 boundary at infinity. There are two s

16、uch metrics: pe-riodically identified anti deSitter space, and Schwarzschild anti deSitter. Only periodicallyidentified anti deSitter space contributes to the boundary to boundary correlation func-tions because the correlation functions from the Schwarzschild anti deSitter metric decayexponentially

17、with real time 8, 9. I take this as indicating that the topologically trivialperiodically identified anti deSitter metric is the metric that interpolates between collapseto a black hole and evaporation. There would be no event horizons and no firewalls.The absence of event horizons mean that there a

18、re no black holes - in the sense of regimesfrom which light cant escape to infinity. There are however apparent horizons which persistfor a period of time. This suggests that black holes should be redefined as metastable boundstates of the gravitational field. It will also mean that the CFT on the b

19、oundary of antideSitter space will be dual to the whole anti deSitter space, and not merely the regionoutside the horizon.The no hair theorems imply that in a gravitational collapse the space outside the eventhorizon will approach the metric of a Kerr solution. However inside the event horizon, them

20、etric and matter fields will be classically chaotic. It is the approximation of this chaoticmetric by a smooth Kerr metric that is responsible for the information loss in gravitationalcollapse. The chaotic collapsed object will radiate deterministically but chaotically. It willbe like weather foreca

21、sting on Earth.That is unitary, but chaotic, so there is effectiveinformation loss. One cant predict the weather more than a few days in advance.31 A. Almheiri, D. Marolf, J. Polchinski, J. Sully, Black Holes: Complementarity or Firewalls?,J. High Energy Phys. 2, 062 (2013)2 S. W. Hawking, Breakdown

22、 of Predicatability in Gravitational Collapse, Phys. Rev. D 14, 2460(1976)3 M. S. Fawcett, The Energy-Momentum Tensor near a Black Hole Commun. Math. Phys. 89,103-115 (1983)4 K. W. Howard, P. Candelas, Quantum Stress Tensor in Schwarzschild Space-Time, PhysicalReview Letters 53, 5 (1984)5 S. W. Hawk

23、ing, Black holes and Thermodynamics, Phys. Rev. D 13, 2 (1976)6 P. Bizon, A. Rostworowski, Weakly Turbulent Instability of Anti-de Sitter Space, Phys. Rev.Lett. 107, 031102 (2011)7 S. W. Hawking, D. N. Page, Thermodynamics of Black Holes in Anti-de Sitter Space, Commun.Math. Phys. 87, 577-588 (1983)8 J. Maldacena, Eternal black holes in anti-de Sitter, J. High Energy Phys. 04, 21 (2003)9 S. W. Hawking, Information Loss in Black Holes, Phys. Rev. D 72, 084013 (2005)4