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**Perspectives on the Origin of the Universe**

3 June 2006 Hawking and Black Holes Prof. K . Y. Michael Wong Outline: The scientist Information and black holes Hawking radiation Detection of black holes Bets on black holes

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The Scientist Born 1942 1st class honours from Oxford, after “not very much work” Symptoms of ALS during Oxford years PhD and Research Fellow in Cambridge Discovered Hawking radiation in 1974 “A Brief History of Time” published in 1987 Numerous honorary degrees and awards Outspoken for world peace, welfare of the handicapped, and other current issues

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**Amyotrophic Lateral Sclerosis**

肌萎縮性脊髓側索硬化症 Also called Lou Gehrig’s disease Symptoms: Difficulty standing, walking, or running Clumsiness – Frequent tripping or falls Difficulty with fine hand motions such as buttoning, writing, turning a key in a lock Atrophy of hand muscles Atrophy of tongue Difficulty chewing food Difficulty swallowing (dysphagia) Difficulty speaking Muscle cramp

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Black Hole Black holes represent the final victory of gravity. A black hole is black because gravity is so strong that light cannot escape. The escape velocity at a distance r from the center of an object with mass M is Light rays The escape velocity increases with mass and decreases with radius. If vescape> c, then light cannot escape and we have a black hole.

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Space Warps If we imagine the spacetime as a “rubber sheet”, then any mass would produce warpings in it. Since black holes produce very strong gravity, spacetime is significantly warped (curved) around them. We see strong light-bending and gravitational redshift.

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The Black Hole Radius For any mass, there is a smallest radius beyond which the object becomes a black hole. This smallest radius rs is called the Schwarzschild radius. Hawking: This defines the size of a black hole, and it depends on the mass only. Anything smaller than its corresponding Schwarzschild radius becomes a black hole.

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**Dissecting a Black Hole**

A non-rotating black hole is particularly simple. There is a point at the center called the singularity (奇點). It has zero size and infinite density. In fact, its properties cannot be described by currently known physics. The event horizon (穹界) is a sphere centered at the singularity with radius equal to the Schwarzschild radius of the black hole. What is inside the event horizon cannot be known by anyone outside because even light cannot escape out. event horizon singularity

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**Event Horizon and Singularity**

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No-hair Theorem Hair here means something complicated (e.g. different styles, colors, perms, etc…). Black holes have no hair because they are simple. Only three things completely characterize a black hole (Hawking 1972): mass angular momentum electric charge

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**Cosmic Censorship Conjecture: Nature Forbids Naked Singularity**

Under general physical conditions, the singularity is enclosed by the event horizon. Information within the event horizon cannot be transmitted to the external world. We say the singularity is concealed or dressed. Those which are not dressed are called naked singularities. Mathematically, naked singularities can exist, but physical considerations suggest cosmic censorship: all singularities are enclosed (Roger Penrose). Hawking bet on cosmic censorship (and conceded too early in 1997).

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Time Arrow One way traffic in Nature? 1. The disintegration of the egg will never happen in the reverse direction (re-integration). 2. Air molecules diffusing out of the bottle will never progress in the reverse direction (infusion).

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**Second Law of Thermodynamics**

There is a very important law in physics, which governs the direction of any process in a physical system. This is called the second law of thermodynamics: The entropy of an isolated system never decrease. Example the reverse is not allowed becomes Smaller entropy Larger entropy

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**The Information Paradox**

If we throw complicated objects (with low entropy) into a black hole, where has the entropy gone? Where has the information escaped from the black hole?

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**Four Laws of Black Hole Thermodynamics**

Bardeen, Carter and Hawking (1973) formulated the four laws of black hole physics, analogous to the four laws of thermodynamics. Second Law The total surface area of black holes is always the same or greater than before. When we throw matter into a black hole, or allow two black holes to merge, the total area of the event horizons will never decrease.

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**Area Theorem time space**

This implies that the surface area of a black hole is a measure of the entropy. If an object has nonzero entropy, then it has a temperature, and it must radiate! At first, Hawking himself could not accept this implication.

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**General Relativity and Quantum Mechanics**

General relativity and quantum mechanics are two major achievements of 20th century physics. General relativity deals with the very large. Quantum mechanics deals with the very small. Physicists attempted to unify the two.

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Hawking Radiation (1974) When Hawking considered quantum mechanics, many of his ideas of black holes need to be changed. Black holes may actually radiate! Near the horizon, particle-anti-particle pairs can be created so that one escapes and the other falls in. Radiation energy follows the blackbody distribution.

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Virtual Particles In classical physics, vacuum means nothing exists. However, in quantum mechanics, vacuum is actually a sea of virtual particles. In quantum mechanics, there is a concept called vacuum fluctuations. Although the average energy of space is zero, local fluctuations of energy are allowed by the Heisenberg uncertainty principle. Energy fluctuations create pairs of particles and antiparticles (e.g. 2 photons). A pair can exist momentarily and is therefore virtual. They annihilate quickly. However, the virtual particles can become real, if the intense curvature of the spacetime of the black hole puts energy to the pair.

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Real Pairs Created Near a black hole, the tidal force is so strong that the virtual pairs are pulled apart. The two virtual particles can become real.

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Hawking Temperature Since the photons can be formed outside the event horizon, they can be emitted away from the black hole. This is called Hawking radiation. The Hawking radiation has a blackbody spectrum, with the temperature given by The temperature is called the Hawking temperature. It decreases with the mass of the black hole.

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Humour: Hawking Style Einstein (on quantum mechanics): God does not play dice with the universe. Bohr (defending quantum mechanics): Einstein should not tell God what to do! Hawking (on radiation from black holes): God not only plays dice but also sometimes throws them where they cannot be seen.

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**Evaporation of Black Holes**

The energy needed to create the real particles comes from the gravitational field of the black hole. Hence, the emission of Hawking radiation reduces the mass of the black hole. As the process continues, the black hole will finally disappear. This is called black hole evaporation. Small black holes have a large tidal force near the event horizon, and the creation of the real particles is easier. Hawking radiation will be more significant. In fact, the time required for evaporation is given by

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**Typical Time of Evaporation**

Black hole with mass about Time for evaporation A man 10-12 seconds A building 4 seconds The Earth 1049 years The Sun 1066 years A galaxy 1099 years For reference, the age of the universe is about 1010 years.

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**Luminosity of Radiation**

For most black holes, the Hawking radiation is too small to be detected. A black hole with detectable Hawking radiation must be very small, with Schwarzschild radius comparable to atomic nucleus. There is no real observational evidence for this kind of black holes so far. These tiny black holes are called primordial black holes, which is believed to be formed in the very early universe. The emission of Hawking radiation reduces the entropy of a black hole. However, the second law of thermodynamics is not violated, since we have to count the entropy of the radiation as well.

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Size Dependence Hawking radiation suggests that black holes must have a finite temperature. The temperature of a black hole is given by The smaller a black hole, the higher the temperature, and therefore the stronger the Hawking radiation. For the primordial black holes, the temperature is extremely high.

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**Detection of Black Holes**

If light cannot escape a black hole, how can we ever find them? Improvements in observational astronomy render the detection of black holes more than a theoretical speculation. Nowadays, we have found many candidates of black holes. Many of them are X-ray binaries.

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天鵝座X-1(雙星系統中的黑洞)

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天鵝座X-1的發現 七十年代發現 72年春，發現HDE226868射電源與X射線源亮度相關 源頭範圍(修正) 源頭範圍(早期)

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確定天鵝座X-1是雙星系統 多普勒效應顯示，雙星系統周期為5.6日 HDE226868的亮度變化顯示，星體因X-1潮汐力變長

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高密度星體? X射線可在極短時間內出現變化，顯示X-1并非中子星 亮度變化受光速限制，顯示X-1很小

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**高密度星體? 引用開普勒定律，顯示X-1質量超過7個太陽質量 中子星質量最高不超過4-5個太陽質量 X-1 不可能是中子星**

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天鵝座 X-1 第一個被發現的黑洞，約有9個太陽質量，所以定是黑洞。

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世紀大賭博 霍金(Stephen Hawking) 賭: 天鵝座X-1不是黑洞 索恩(Kip Thorne) 賭: 天鵝座x-1是黑洞

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**Baby Universes in Black Holes**

In 1980s, Thorne thought about wormholes, and Hawking thought about baby universes. If an object falls into a black hole, it could go to an independent baby universe. Science fiction? Can one travel to the past or another universe? Beware of spaghettification! Implication: there can be information loss in black holes. In 1992, Hawking concluded that the universe is “safe for historians”.

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Another Bet In 1997, Hawking and Thorne bet with Preskill on the black hole information paradox. Hawking and Thorne: The information crossing into the event horizon of a black hole is lost to our universe; the black hole emits the same radiation regardless of what falls into it. Preskill: The information will be eventually released. In 2004, Hawking conceded and admitted that black holes eventually transmit, in a garbled form, information about all matter they swallow. Preskill was awarded an encyclopedia of baseball, from which “information can be recovered at will”.

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Conclusion Hawking’s contribution to the theory of black holes (structure, no hair theorem, radiation, information and entropy). Hawking’s work is confirmed by experiments (Cygnus X-1). Hawking’s openmindedness (bet concessions). Hawking’s attitude towards life (adversity, science, humour). Hawking’s eagerness to popularize science.

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