Class 26 : Exotica in space: Wormholes and timewarps

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Class 26 Exotica in space Wormholes and
timewarps

• Wormholes
• The wormhole inside of black holes
• How to build a stable wormhole
• Timewarps
• The idea of cause and effect
• The assumption of causality and the speed of
  light
• Can time-machines exist?

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Astrophysicists view of black holes stops at the
event horizon
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But there is structure inside the event horizon!
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The Schwarzschild solution

• Schwarzschild solution
• Mathematical description of a non-rotating and
  non-charged black hole
• Discovered by Karl Schwarschild in 1916
• Any normal particles/light entering event horizon
  are doomed to hit singularity
• Once at the singularity, they will be destroyed
  at the quantum level
• But, the Schwarzschild solution has an
  interesting mathematical structure
• Suggests that particles traveling faster than
  speed of light can avoid the singularity
• Then pass through a wormhole and emerge from a
  white hole into a new region of normal space
• Schwarzschild throats

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• Do Schwarschild black holes really exist?
  Probably not
• Real stars do not form Schwarzschild black holes
  (they rotate!)
• Full Schwarzschild solution needs existence of
  white hole these violate 2nd law of
  thermodynamics.
• Even if they did exist, they are unstable! You
  couldnt pass through it without having it
  collapse on you!

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The Kerr solution

• Kerr solution
• Mathematical solution describing rotating
  (non-charged) black holes
• Applicable to most real black holes in nature
• Discovered by Roy Kerr in 1960s
• More interesting than Schwarschild solution
• This time, dont need to travel faster than light
  to avoid the singularity!
• Singularity has a ring structure enter the
  wormhole by flying through the ring
• Are then propelled from a white hole and emerge
  into another region of normal space.

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• Do these really exist? Again, seems unlikely
• White holes still violate thermodynamics
• Wormhole still unstable
• Some researchers dont even think that there is a
  hole in the ring-singularity!

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Scientific American, Jan 2000
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• Can we build a stable wormhole?
• Some work has shown that we need to use very
  unusual matter negative energy matter.
• Such stuff probably doesnt exist!
• But, were still learning about the basic
  structure of space and time
• Physics that is currently unknown might
  eventually allow wormholes to be made (either by
  us or by nature)!

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Scientific American, Jan 2000
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II Time Machines

• Idea of cause and effect
• Foundation of scientific reasoning
• If one event can have an effect on the other
  event, they are said to be causally-connected.
• To have any meaning, the cause must happen before
  the effect!
• This requirement is called causality.
• Einsteins theory of special relativity
• Suppose that a signal can be transmitted at
  faster than the speed of light
• Then Einsteins Special Theory of Relativity
  shows that you can change the order of
  causally-connected events.
• Can make effect happen before cause!
• We disallow this! It violates causality.
• Thus, we have to postulate that no signal can
  travel faster than the speed of light.

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• The big question Does Einsteins theory
  necessarily demand causality?
• Not at all obvious!
• Again probably have to understand the nature of
  space-time a lot better than we currently do.