Black Holes

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Black Holes
Eternal? Or just long lived?
by Patrick Murphy
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A Brief History Of Black Holes.

• First proposed in thought experiment by John
  Mitchell in 1783
• 1916 Karl Schwarzschild solves Einsteins field
  equation for spacetime around a spherical body.
• A little more on Einstein.

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General Relativity

• Published in 1915
• Describes the relationship between mass and
  spacetime.
• Spacetime tells mass how to move and mass tells
  spacetime how to curve.
• Confirmed in 1919 by Arthur Eddington

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Spacetime

• Apparent vs. real trajectory of a light beam

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Karl Schwarzschild

• Solved metric for spacetime surrounding a
  spherical mass.
• Schwarzschild metric

• Schwarzschild radius

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Classic Black Holes

• 1939 Oppenheimer shows massive stars collapse
  to a singular point.
• Multiple solutions involving small perturbations
  confirm results.
• Singularity surrounded by event horizon, point of
  no return.
• Three parameters Mass, Charge and Spin

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Classic Black Holes

• Roger Penrose
• 1969 Proved all full gravitational collapses
  result in a singularity
• Postulated Cosmic Censorship Law

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2 main types

• Schwarzschild
• Static, no rotation
• Point-like singularity
• Event Horizon

• Kerr
• Rotates
• Ring shaped singularity
• Inner Horizon
• Outer Horizon
• Ergosphere

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2 main types

• Schwarzschild

• Kerr

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• So nothing can escape the gravitational
  attraction of the black hole once past the event
  horizon?

• Classically, yes

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Problems with classical theory

• Assumed TBH 0 K, despite mathematical evidence
  to the contrary .
• No thermal spectrum
• Singularity too small for Relativity

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Can Black Holes Radiate?

• Maybe so
• 1970 Jacob Berkenstein suggests area of event
  horizon is a measurement of black holes entropy.
• 1970 Stephen Hawking shows that area of event
  horizon always increases.
• 1971 Borisovitch Zeldovitch claims rotating
  black holes radiate until they stop spinning .

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1974 Hawking Radiation

• Hawking repeats Zeldovitchs calculatons.
• Agrees except.
• Finds they continue to radiate!
• Theres more
• His solution predicted the emission spectrum to
  be exactly that of a hot body.
• That means temperature and entropy

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How can it radiate?

• Various mechanisms are possible, depending on
  your frame of reference.
• They all acknowledge quantum vacuum fluctuations
  as source.
• Quantum vacuum fluctuations are unavoidable due
  to Heisenbergs Uncertainty Principle

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And?

• Say youre safely at rest, watching vacuum
  fluctuations.
• You see a virtual pair of photons created just
  outside the event horizon.
• Tidal gravity pulls them apart, they become real.
• One gets sucked in, the other escapes forever.

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So Whats Left?

• Resolution of the Information paradox
• Development of an adequate quantum theory of
  gravity, Relativity is no longer a valid
  approximation on scales smaller than the Planck
  length, lp (hG/2pc3)1/2 .

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Information loss?

• In technical jargon, the black hole has performed
  a non-unitary transformation on the state of the
  system.  As you may recall, non-unitary evolution
  is not allowed to occur naturally in a quantum
  theory because it fails to preserve probability.
• Hawking suggests that black hole radiation
  contains information about what went in, albeit
  in a mangled form.

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Branes?

• P brane length in p dimensions
• P 1 String
• P 2 Membrane
• Etc
• Information stored

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Quantum Gravity?

• Singularities are tiny
• Quantum foam
• No time, how space manifests itself is
  probabilistic
• Many candidates, include M-theory,
  Supergravity, AdS/CFT , holography

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So Why study Black holes?

• Black holes push the limits of physical theories
• Among the most extreme phenomena in the universe
• I think theyre cool.
• Thats it
• Thanks for listening
• The End
• (applause. please?)

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References

• Kip Thorne, Black Holes And Timewarps (Norton,
  1994)
• Eric Poisson, A Relativist's Toolkit, The
  mathematics of black hole mechanics (Cambridge
  University Press, 2004).
• Alessandro Fabbri and Jos\'e Navarro-Salas,Model
  ing Black Hole Evaporation (Imperial College
  Press, 2005)
• John A. Wheeler, E.F. Taylor, Exploring Black
  Holes, Introduction to General Relativity
  (Addison Wesley, 2000)
• Stephen Hawking, The Universe In A Nutshell
  (Bantam, 2001)

• Images
• http//chandra.harvard.edu/resources
• http//www.belmontnc.4dw.net/DWFNEU5.gif
• www.tqnyc.org/NYC040808/ neutron_star.jpg
• http//en.wikipedia.org
• www.scienceweek.at