Black Holes, part II

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Black Holes, part II
Jaldert van der Werf
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Contents

• Curvature space-time
• Light Deflection
• Centrifugal forces
• Event horizon
• Quantities of black holes
• Rotating black holes
• Charged black holes

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Curved spacetime of black holes

• Spacetime is curved by matter.
• If fixed mass contracts, its surface gravity
  increases.
• At critical size space-time becomes so curved it
  entirely encloses the body.
• Schwarzschild radius.

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Curved spacetime of black holes (2)
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Light Deflection

• Light rays leaving a gravitating body are curved.
• The smaller the body the more light rays are
  curved.
• If radius of body is less then photon sphere, the
  exit cone closes.
• Rays within the cone escape, those outside the
  cone fall back.

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Light Deflection (2)
light rays
star
Star larger than photon sphere
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Light Deflection (3)
Star almost the size of photon sphere
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Light Deflection (4)
exit cone
Stars smaller than photon sphere
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Centrifugal Forces

• Far away from black hole
• Light rays travel in nearly straight lines
• Object pushed outward by centrifugal force

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Centrifugal Forces (2)

• At event horizon
• Light rays are bent in perfect circles
• No centrifugal force

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Centrifugal Forces (3)

• Close to black hole
• Light rays are curved so much that tube seems to
  curve away
• Object pushed inward by centrifugal force

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Centrifugal Forces (4)

• Two spacecrafts can be used to measure
  centrifugal force
• One spacecraft is stationary, experiencing no
  centrifugal force
• The other craft is moving in the same orbit.

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Event Horizon
Light rays or objects that pass the horizon cant
go back. But theres nothing special to notice at
the horizon. The event horizon is the
Schwarzschild radius.
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Event Horizon (2)

• If you pass the event horizon nothing special
  happens from your point of view.
• In your spacetime it takes a fixed time to reach
  the singularity (Schwarzschild radius divided by
  the speed of light).
• For a distant observer it takes an infinite time
  for you to reach and enter the black hole.

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Event Horizon (3)

• A distant observer sees an object slowing down
  when it approaches the event horizon.
• The object slows to a halt at the horizon.
• For the observer the object doesnt pass the
  horizon.

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Event Horizon (4)

• Object approaches singularity.
• Object is stretched along the radius of the black
  hole.
• Object is compressed in directions perpendicular
  to this axis.
• Caused by tidal forces.
• Phenomena is called spaghettification.

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Event Horizon (5)
Spaghettification of objects falling towards a
planet.
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Event Horizon (6)
Outside the horizon light cones point upward,
forward in time. Inside light cones tip so that
light falls into the black holes center.
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Quantities of a black hole

• Only three quantities to characterize a black
  hole
• Mass
• Angular momentum (rotation)
• Electric charge

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Different types

• Static black hole
• Schwarzschild
• Charged black hole
• Kerr-Newman if rotating
• Reissner-Nordström if static
• Rotating black hole
• Kerr

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Rotating black hole
At the static-surface space flows with the speed
of light. A particle is dragged along a the speed
of light, relative to the distant observer.
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Rotating black hole (2)

• In the ergosphere space flows faster than the
  speed of light.
• The inward radial component of velocity of the
  flow is less than the speed of light.
• Particles can still escape, because there not in
  the event horizon.
• A particle can escape by gaining energy of the
  spin of the black hole.

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Charged black holes

• Strong concentrations of electric charge are rare
  in astronomy.
• Electrically charged objects are easily
  neutralized by charged particles in the
  interstellar medium.
• Electromagnetic repulsion is far stronger than
  gravitational attraction.
• Charged black holes are not expected to form in
  nature.

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Conclusions

• Spacetime around a black hole encloses its entire
  body.
• Nothing can escape from the singularity if it
  passes the event horizon.
• Most black holes rotate.
• Charged black holes are not expected to form in
  nature.

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Literature

• Book
• Cosmology Science of the Universe 2nd edition,
  by Edward Harrison
• Scientific American
• Black Holes and the Information Paradox
• Black Holes and the Centrifugal Force Paradox
• Internet
• http//math.ucr.edu/home/baez/physics/Relativity/B
  lackHoles/fall_in.html
• http//en.wikipedia.org/wiki/Black_hole
• http//en.wikipedia.org/wiki/Rotating_black_hole
• http//en.wikipedia.org/wiki/Charged_black_hole
• http//en.wikipedia.org/wiki/Spaghettification

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End of part II
Questions?