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## Black Holes

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### Black Holes Matthew Trimble 10/29/12 History Einstein Field Equations published in 1915. Karl Schwarzschild: physicist serving in German army during WW1. – PowerPoint PPT presentation

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Title: Black Holes

1
Black Holes
• Matthew Trimble
• 10/29/12

2
History
• Einstein Field Equations published in 1915.
• Karl Schwarzschild physicist serving in German
army during WW1.
• Solved EFE for a non- rotating, spherical source,
and wrote a paper on quantum theory while
suffering from pemphigus on Russian front.
• His solution is called the Schwarzschild Metric.

3
Schwarzschild Metric
4
Schwarzschild Metric
• Same metric can describe non- rotating black
holes.
• r Schwarzschild radius- the event horizon of
the black hole.
• r 2GM/c2
• Observers outside cannot view events inside.
• 3km for the Sun, 9mm for the Earth.

5
Black Hole Formation
• Once matter is compressed smaller than r,
collapse occurs, forming a black hole.
• The kind of pressures needed to do this are
typically found in Type II Supernova explosions.
• r is the point at which an objects escape
velocity is c, meaning nothing can come back out.

6
Vacuum Energy
• In empty space, pairs of particle-antiparticle
pairs appear and annihilate on the Planck
timescale 5.39X10-44 s
• Because this happens so quickly, this does not
violate the Uncertainty Principle.
• The short lifetime gives these particles the name
Virtual Particles.

7
• Near a black hole, time is dilated enough that
these virtual particles last longer than the
Planck timescale.
• One particle can be released away from the black
hole, while the other falls in.
• By measuring positive energy particles, the
particle with negative energy had to fall into
the singularity, lowering the mass and energy of
the black hole.

8
Shrinking
• Because the blackbody temperature is inversely
proportional to the mass, the Hawking Radiation
causes the black hole to shrink.
• This proportionality also means that a very
massive black hole radiates weakly, and can
easily overcome this loss through accretion.

9
Mini Black Holes
• With a very small M, these Hawking radiate very
quickly, meaning they will evaporate long before
they have a chance to accrete matter and grow
large.

10
Bekenstein-Hawking Entropy
• Derived using the blackbody temperature of
• Entropy is also proportional to the number of
microstates.
• For a black hole, these microstates are the
number of ways a quantum black hole could be
formed.
• The B-H Entropy method agrees with M theorys
prediction of the quantum states in a black hole.

11
Falling Inside a Black Hole
• Observers P.o.V you freeze at the event
horizon, along with anything else the black hole
has every accreted.
• Your P.o.V youre time is the proper time (no
redshift), so you go right past r.
• This is because the r/r is a coordinate
singularity, not a physical singularity.

12
Eddington-Finkelstein Coordinates
• Singularity at rr vanishes.
• The lnr-r term in the coordinates defines a
one way membrane.
• For advanced coordinates, particles can only fall
in.
• For retarded coordinates, particles can only move
out, theoretically defining a White Hole.

13
Conclusion
• Karl Schwarzschild was more dedicated to physics
than you ever will be.
• Black Holes are interesting objects that require
an abstract way of thinking in order to explain
them mathematically.

14
References
• http//en.wikipedia.org/wiki/Schwarzschild_metric
• http//en.wikipedia.org/wiki/Vacuum_energy
• http//en.wikipedia.org/wiki/Einstein_field_equati
ons
• http//en.wikipedia.org/wiki/Karl_Schwarzschild
• Relativity, Gravitation, and Cosmology, Second
Edition, Ta-Pei Cheng
• PHZ4601 Lecture Notes, Fall 2012, Dr. Owens