Download Hawking and Black Holes

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
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
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
Black Hole
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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
2GM
v escape 
r
The escape velocity increases with mass
and decreases with radius.
If vescape> c, then light cannot escape and
we have a black hole.
Light
rays
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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
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.
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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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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.
S  0
Example
Smaller entropy
Larger entropy
becomes
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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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
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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
c
k BTbh 
4Rs
 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
3
tevap
 M 
 10  12  years
 10 kg 
10
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Typical Time of Evaporation
Black hole with mass
about
A man
Time for
evaporation
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
 M sun 

Tbh  10 
 M bh 
7
 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
•時至今日，已有95%把握確定X-1是黑洞
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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)
索恩(Kip Thorne)
賭: 天鵝座X-1不是黑洞
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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