霍金的偉大不在於他提出黑洞理論，在勇於自我批評， 但。。。

公孫明 03/17/2018

霍金的偉大，不在於他提出黑洞理論，在於他勇於自我批評，但更偉大的是，他從21歲起就已是個漸凍人，卻能夠克服種種困難生存到76歲。

他對生命的尊重，熱愛，和執着，以及那種永不退縮的毅力和與逆境鬥爭的精神，才是值得我們學習的對象。

以研究「黑洞」着名的物理學家霍金，2014年1月22日在網路上發表一篇名為《黑洞的信息保存與氣象預報》（Information Preservation and Weather Forecasting for Black Holes）的最新論文：

Information Preservation and Weather Forecasting for Black Holes

https://genius.com/Stephen-hawking-information-preservation-and-weather-forecasting-for-black-holes-annotated

S. W. Hawking

(Submitted on 22 Jan 2014)

Abstract

It has been suggested [1] that the resolution of the information paradox for evaporating black holes is that the holes are surrounded by firewalls, bolts of outgoing radiation that would destroy any infalling observer. Such firewalls would break the CPT invariance of quantum gravity and seem to be ruled out on other grounds. A different resolution of the paradox is proposed, namely that gravitational collapse produces apparent horizons but no event horizons behind which information is lost. This proposal is supported by ADS-CFT and is the only resolution of the paradox compatible with CPT. The collapse to form a black hole will in general be chaotic and the dual CFT on the boundary of ADS will be turbulent. Thus, like weather forecasting on Earth, information will effectively be 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, August 2013

Some time ago [2] I wrote a paper that started a controversy that has lasted until the present day. In the paper I pointed out that if there were an event horizon, the outgoing state 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 from an initial pure state to a mixed final state and a loss of unitarity. On the other hand, the ADS-CFT correspondence indicates that the 7evaporating black hole is dual to a unitary conformal field theory on the boundary of ADS. This is the information paradox.

Recently there has been renewed interest in the information paradox [1]. The authors of [1] suggested that the most conservative resolution of the information paradox would be that 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 located at the event horizon, the position of the event horizon is not locally determined but is a function of the future of the spacetime.

Another objection is that calculations of the regularized energy momentum tensor of matter fields are regular on the extended Schwarzschild background in the Hartle-Hawking state [3, 4]. The outgoing radiating Unruh state differs from the Hartle-Hawking state in that it has no incoming radiation at infinity. To get the energy momentum tensor in the Unruh state one therefore has to subtract the energy momentum tensor of the ingoing radiation from the energy momentum in the Hartle-Hawking state. The energy momentum tensor of the ingoing radiation is singular on the past horizon but is regular on the future horizon. 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 holes in asymptotically flat space, then they should also form around black holes in asymptotically anti deSitter space for very small lambda. One would expect that quantum gravity should be CPT invariant. Consider a gedanken experiment in which Lorentzian asymptotically anti deSitter space has matter fields excited in certain modes. This is like the old discussions of a black hole in a box [5]. Non-linearities in the coupled matter and gravitational field equations will lead to the formation of a black hole [6]. If the mass of the asymptotically anti deSitter space is above the Hawking-Page mass [7], a black hole with radiation will be the most common configuration. If the space is below that mass the most likely configuration is pure radiation.

Whether or not the mass of the anti deSitter space is above the Hawking-Page mass the space will occasionally change to the other configuration, that is the black hole above the Hawking-Page mass will occasionally evaporate to pure radiation, or pure radiation will condense into a black hole. By CPT the time reverse will be the CP conjugate. This shows that, in this situation, the evaporation of a black hole is the time reverse of its formation (modulo CP), though the conventional descriptions are very different. Thus if one assume quantum gravity is CPT invariant, one rules out remnants, event horizons, and firewalls.

Further evidence against firewalls comes from considering asymptotically anti deSitter to the metrics that fit in an S1 cross S2 boundary at infinity. There are two such metrics: pe- riodically identified anti deSitter space, and Schwarzschild anti deSitter. Only periodically identified anti deSitter space contributes to the boundary to boundary correlation func- tions because the correlation functions from the Schwarzschild anti deSitter metric decay exponentially with real time [8, 9]. I take this as indicating that the topologically trivial periodically identified anti deSitter metric is the metric that interpolates between collapse to a black hole and evaporation. There would be no event horizons and no firewalls.

The absence of event horizons mean that there are no black holes - in the sense of regimes from which light can’t escape to infinity. There are however apparent horizons which persist for a period of time. This suggests that black holes should be redefined as metastable bound states of the gravitational field. It will also mean that the CFT on the boundary of anti deSitter space will be dual to the whole anti deSitter space, and not merely the region outside the horizon.

The no hair theorems imply that in a gravitational collapse the space outside the event horizon will approach the metric of a Kerr solution. However inside the event horizon, the metric and matter fields will be classically chaotic. It is the approximation of this chaotic metric by a smooth Kerr metric that is responsible for the information loss in gravitational collapse. The chaotic collapsed object will radiate deterministically but chaotically. It will be like weather forecasting on Earth. That is unitary, but chaotic, so there is effective information loss. One can’t predict the weather more than a few days in advance.

[1] 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 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, Physical Review Letters 53, 5 (1984)
[5] S. W. Hawking, 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)

下邊是有關霍金對黑洞理論的中文前後解釋：

“英國着名物理學家史蒂芬霍金（Stephen Hawking），以其「黑洞理論」聞名於世，更啟發現代外太空探險和好萊塢科幻電影，但他日前發表的最新論文卻推翻「黑洞理論」，宣稱黑洞（Black holes）其實不存在，真實存在的是「灰洞」（Grey holes）。

黑洞指的是宇宙中星體爆炸時，四周會產生強大的引力，並在宇宙空間中產生黑洞，把附近的一切都吞噬，包括光線和物質。由於引力相當強大，被吸入的物質以比光速更快的速度被吸入黑洞，同時永遠無法從黑洞邊緣（或稱「視界」）逃出。

文中表示由於找不到黑洞的邊界，因此黑洞根本可被視為不存在。

他還說，物質和能量在被黑洞困住一段時間以後，是可以被重新釋放到宇宙中的。他在論文中承認，自己最初有關視界的認識是有缺陷的，光線其實是可以穿越視界的。霍金同時指出，對於這種逃離過程的解釋需要一個能夠將重力和其他基本力成功融合的理論。在過去近一百年間，物理學界都未曾有人試圖解釋這一過程。

1976年霍金發表「霍金輻射」理論，該理論認為在「霍金輻射」的影響下，黑洞會濃縮並蒸發。當黑洞消失後，黑洞形成初始最核心的「奇點」也會隨之消失。但這種說法與量子力學相關理論出現相互矛盾之處，因為現代量子物理學認定「奇點」是永遠不會完全消失的。這便是所謂的「黑洞悖論」。

30多年來，霍金試圖以各種推測來解釋這一悖論。霍金曾指，黑洞中量子運動是一種特殊情況，由於黑洞中的引力非常強烈，量子力學在此時已經不適用了。但一直以來，他的這種看法並未被物理學界廣泛接受。

現在看來，霍金終於給了這個矛盾觀點一個更具說服力的答案。霍金稱，黑洞從來都不會完全關閉自身，它們在一段漫長的時間裡逐步向外界輻射出越來越多的熱量，最終黑洞會開放自己並釋放出其中包含的物質能量。所以，所謂的黑洞，更像是「灰洞」。

「灰洞」一詞本已存在於物理學界。它出現於1993年，美國波士頓大學的布雷徹將「灰洞」定義為：大質量星的坍縮不足以形成黑洞，但有可能形成比典型中子星有較小的半徑和較大密度的星體。“