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
Hawking Radiation

• 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
  Hawking radiation.
• 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