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Black Holes


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

Black Holes
  • Matthew Trimble
  • 10/29/12

  • 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.

Schwarzschild Metric
Schwarzschild Metric
  • Same metric can describe non- rotating black
  • 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.

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.

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.

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.

  • 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.

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

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

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.

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
  • For retarded coordinates, particles can only move
    out, theoretically defining a White Hole.

  • 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.

  • http//
  • http//
  • http//
  • http//
  • Relativity, Gravitation, and Cosmology, Second
    Edition, Ta-Pei Cheng
  • PHZ4601 Lecture Notes, Fall 2012, Dr. Owens
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