霍金与黑洞学说【英文】Hawking

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The Black Hole Radius
2GM rs 2 c


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.
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
v escape

2GM r
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.
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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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).
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
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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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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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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.
3 June 2006
Hawking and Black Holes
Outline: The scientist Information and black holes Hawking radiation Detection of black holes Bets on black holes
The Scientist
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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.
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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.
S 0
Example Smaller entropy becomes Larger entropy
the reverse is not allowed
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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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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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Hawking Radiation (1974)

When Hawking considered quantum mechanics, many of his ideas of black holes need to be changed.
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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Dissecting a Black Hole
• A non-rotating black hole is particularly event horizon 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. singularity
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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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