Transcript Slide 1
Black Holes
Eternal? Or just long lived?
by Patrick Murphy
A Brief History Of Black
Holes.
• First proposed in thought experiment by John
Mitchell in 1783
• 1916: Karl Schwarzschild solves Einstein’s field
equation for spacetime around a spherical
body.
• A little more on Einstein….
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
Spacetime:
• Apparent vs. real trajectory of a light beam
Karl Schwarzschild
• Solved metric for
spacetime surrounding
a spherical mass.
• Schwarzschild metric :
ds = 1/(1-2M/r)dr + r d - 1/(1-2M/r)dt
2
2
2
2
• Schwarzschild radius :
R = 2GM/c
2
2
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
Classic Black Holes
Roger Penrose
• 1969: Proved all full
gravitational
collapses result in a
singularity
• Postulated Cosmic
Censorship Law
2 main types
Schwarzschild
Kerr
• Static, no rotation
• Point-like singularity
• Event Horizon
•
•
•
•
•
Rotates
Ring shaped singularity
Inner Horizon
Outer Horizon
Ergosphere
2 main types
Schwarzschild
Kerr
So nothing can escape the
gravitational attraction of the
black hole once past the event
horizon?
Classically, yes
Problems with classical
theory
• Assumed TBH = 0 K, despite
mathematical evidence to the
contrary .
• No thermal spectrum
• Singularity too small for
Relativity
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 Zel’dovitch claims rotating
black holes radiate until they stop spinning .
1974: Hawking Radiation
• Hawking repeats Zel’dovitch’s
calculatons.
• Agrees except….
• Finds they continue to radiate!
• There’s more…
• His solution predicted the
emission spectrum to be exactly
that of a hot body.
• That means temperature and
entropy
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
Heisenberg’s Uncertainty
Principle
And…?
• Say you’re 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.
So WhAt’S 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/2πc3)1/2 .
Information loss?
• In technical jargon, the black hole has
performed a non-unitary transformation on the
state of the system. As you may recall, nonunitary 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.
Branes?
• P brane: length in p
dimensions
• P = 1 : String
• P = 2 : Membrane
• Etc…
• Information stored
Quantum Gravity?
• Singularities are tiny
• Quantum foam
• No time, how space
manifests itself is
probabilistic
• Many candidates, include :
M-theory, Supergravity,
AdS/CFT , holography …
So Why study Black
holes?
• Black holes push the limits of physical theories
• Among the most extreme phenomena in the
universe
• I think they’re cool.
• That’s it
• Thanks for listening
• The End
• (applause…. please?)
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,Modeling 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 :
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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