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Hawking and Black Holes

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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
                  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
   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                Light
                           v escape                       rays
                                         r
 The escape velocity increases with mass
  and decreases with radius.
 If vescape> c, then light cannot escape and
  we have a black hole.


                                                                    4
                  Space Warps
 Ifwe 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.


                                5
        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.




                                                               6
         Dissecting a Black Hole
• A non-rotating black hole is particularly
  simple.                                               event horizon
• 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

                                                                 7
Event Horizon and Singularity




                                8
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



                                                9
     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).


                                                          10
                     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).
                                                              11
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


                                                                12
                  the reverse is not allowed
     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?




                                                     13
         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.



                                                           14
                 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.
                                                            15
16
           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.




                                                           17
       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.




                                                               18
                 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.
                                                               19
              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.




                                                              20
          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.




                                                            21
         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.



                                                           22
     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
                             M 
                 tevap  10  12  years
                         10
                             10 kg 
                                   

                                                             23
   Typical Time of Evaporation
     Black hole with mass             Time for
            about                    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.
                                                              24
         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.

                                                              25
               Size Dependence
Hawking radiation suggests that black holes must have a finite
temperature. The temperature of a black hole is given by
                               M sun 
                              M 
                     Tbh  10 
                             7
                                      
                               bh 
 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.




                                                             26
       Detection of Black Holes
 Iflight 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.




                                                      27
天鵝座X-1(雙星系統中的黑洞)




                   28
           天鵝座X-1的發現
             七十年代發     72年春,發現
             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)




                              29
 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
                            30
       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




                31
        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


                          32
      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。
                 33
                      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




                                           34
    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”.
                                          35
                    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”.


                                                             36
                     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.




                                                             37

				
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