General Relativity: Part II

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General Relativity Part II

• Gravity is Curved Space

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• 1) You walk 10 km south, 10 km west and then 10
  km north and you are back where you started.
• What colour is the bear?
• a) brown b) black c) white

Hint There is only one place in the world where
this would happen.
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• We live in a 4-dimensional curved space which we
  cannot see or experience directly.
• We can get a sense of how it works by using an
  analogy with fewer dimensions.

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• Imagine that you are a smart blind ant moving
  about on the surface of a balloon. Draw the path
  of the polar explorer from the the riddle on your
  balloon.
•  

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• 2) Suppose that there is a light at the North
  Pole. The light radiates in all directions and
  follows the straightest lines in this space. What
  will an ant at the South Pole notice?
• a)      Nothing.
• b)      A bright spot.
• c)      A bright ring.
•  

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The curved arcs that you see in this photograph
are coming from a distant light. Between it and
the Earth there is a large mass that warps the
space, so that light appears to come from many
directions.
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• We can detect how mass distorts the three
  dimensions of space but we cant picture it.

4) How would an ant explain this motion?
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• When Einstein first calculated the curvature of
  light he got it wrong by a factor of two. Half
  the curvature is from the equivalence principle
  and the second half is from the curvature of
  space.

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• Mass curves spacetime into gravitational lenses.

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• Gravitational lenses are used by astronomers to
  measure the mass of regular matter and dark
  matter.

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• Draw a 15-cm line on your balloon. At right
  angles to that, draw another 15-cm line. Draw two
  more of them. What do you get?

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• Planetary orbits dont form simple ellipses
  either. They form patterns like Daisy petals -
  this is called the precession of the equinoxes.
  This was a known problem with Newtonian
  Gravitation that General Relativity was able to
  solve.

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• 5) The planet with the greatest precession will
  be
• a)      Jupiter because it is biggest
• b)      Mercury because it is smallest
• c)      Mercury because it is closest to the
  sun
• d)      Neptune because it is farthest

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• Suppose, the balloon was expanding.
• What would the ant notice?

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The galaxies are all moving away from us and the
more distant ones are moving faster.
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• There is a simple relationship between velocity
  and distance. This suggests that everything in
  the universe was once gathered in one point that
  exploded around 14 billion years ago the Big
  Bang.

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• 6) Gravity should cause this expansion to
• a) slow down b) speed up c) remain constant.

Best-fit
Constant velocity
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• 7)As a stars life ends, it collapses and gets
  much denser. What would you see if you got close
  to dense star whose escape velocity was almost c?
• a) Light rising and falling
• b) Faint radio waves
• c) Faint gamma rays

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• 8) What happens if the escape velocity is
  greater than c?
• a) only gamma rays escape
• b) only radio waves escape
• c) nothing escapes
• d) nothing escapes so it cant be detected

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• You can detect one by the way it warps light.

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• You can detect black holes that have matter
  spiraling into them. This matter will form hot
  disks that give off x-rays.

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• Black Holes often produce jets spewing matter
  out at speeds close to c. Many of these have been
  found.

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Black holes can also be detected by measuring
the speeds of orbiting bodies. This data can be
used to calculate the mass and density of the
central body.
M v2 r /G
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• What is it like inside a Black Hole? All light
  and matter will be driven by the extremely curved
  spacetime into a singularity of infinite density.
  

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• Rapidly orbiting massive objects should generate
  gravitational waves, ripples in the fabric of
  space.
• These waves take energy away, so the objects
  should spiral into the center.

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• Taylor and Hulse have measured a binary pulsar
  doing exactly that.

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• Large detectors are being built around the world
  to detect gravitational waves directly.
• This is LIGO.

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• An even larger gravity detector called LISA, is
  being built. It is made of three satellites in a
  huge triangle. It may be able to measure the
  curvature near a Black Hole.