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Black Holes


Black Holes Newtonian Universal Mutual Gravitation Isaac Newton, in his Principia, formulated the Law of Universal Mutual Gravitation: Gravity is an Attractive force ... – PowerPoint PPT presentation

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Title: Black Holes

Black Holes
  • Universal Mutual Gravitation Isaac Newton, in his
    Principia, formulated the Law of Universal Mutual
  • Gravity is an Attractive force
  • Works to bring massive objects closer together.
  • Gravity is a Universal force
  • Works everywhere in the Universe.
  • Gravity is a Mutual force
  • Works between pairs of massive objects

  • Gravitational Force Force of gravity between any
    two objects depends only upon
  • The masses of the two objects
  • More massive objects feel a stronger force.
  • The distance between them
  • Objects closer together feel a stronger force.
  • It does not depend at all on the shapes, colors,
    or compositions of the two objects.

  • The Law of Universal Gravitation The force of
    gravitational attraction between any two massive
    bodies is proportional to their masses and
    inversely proportional to the square of the
    distance between their centers.
  • The Force of Gravity is an example of an "Inverse
    Square Law Force"

  • Stated Mathematically
  • Where
  • F force due to gravity.
  • M1 mass of the first object
  • M2 mass of the second object
  • d distance between their centers.
  • G "Gravitational Force Constant"

The Flaw
  • Doesnt work when you are talking about intense
    gravitational force of black holes and neutron
  • Thankfully Einstein created the principles of

  • In Newtonian gravitation, an orbit is always an
  • As the gravitating body becomes more massive and
    the test particle orbits it more closely, the
    speed of the particle in its orbit increases
    without bound, always balancing the gravitational
    force. For a black hole, Newton's theory predicts
    orbital velocities greater than the speed of

1st Flaw
  • It gave the wrong prediction for the precession
    of the perihelion of Mercury's orbit.
  • Mercury's orbit is elliptical, as predicted by
    Newton's theory of gravity, but the ellipse
    doesn't stay in precisely the same place all the
  • It precesses, which is to say that as Mercury
    orbits the sun, the entire ellipse rotates about
    the focal point (i.e. the sun) as shown in the in
    the picture

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2nd Flaw
  • It did not explain why the gravitational force on
    an object was proportional to its inertial mass.
  • In other words it did not explain why
    gravitational acceleration is independent of the
    mass or composition of an object.

3rd Flaw
  • It was inconsistent with the Special Theory of
    Relativity. That is, if an instantaneous force of
    gravitational attraction exists between two
    objects then information about the location of
    one object would be transmitted to another object
    instantaneously by changes in the gravitational
    force. Thus it would be possible to send
    information faster than the speed of light.

The special theory of relativity changes our
conceptions of space and time
  • This theory, published by Einstein in 1905, is
    based on the notion that there is no such thing
    as absolute space or time
  • Space and time are not wholly independent of each
    other, but are aspects of a single entity called

Special Relativity
  • General Relativity developed from Special
  • universal speed limit speed of light c
    300,000 km/sec
  • Example A Nolan Ryan on a train
  • train moves East at vtrain 30 m/sec (70 mph)
  • Nolan, who is on the train, throws his fastball
    at vball 40 m/sec (90 mph)
  • Nolan sees the ball move at vball 40 m/sec (90
  • We see the ball move at vtrainvball 70 m/sec
    (160 mph) from the ground

  • Example B Nolan switches on a flashlight
  • Nolan turns on his flashlight pointing East
  • Nolan sees the light move at c 300,000 km/sec
  • Do we see the light move at vtrainc 300,000.03
    km/sec? NO!!
  • We also see the light move at exactly c 300,000
  • Even if the train moved at vtrain 200,000
    km/sec, we'd still see the light move at velocity

  • Time reversed case now lets throw a baseball up
    from the Earth (ignoring air friction)
  • I throw it at 20 m/sec - it goes up 20 m and
    falls back to Earth
  • Nolan Ryan throws it at 40 m/sec - it goes up to
    80m at falls back to Earth
  • shoot it out of a cannon at 10 km/sec - it goes
    out beyond the communication satellites and then
    falls back to Earth
  • shoot it out of a cannon at 11 km/sec - and it
    goes up and slows down, but never comes back
  • This is the escape velocity

The speed of light is the same to all observers,
no matter how fast they are moving
An observer will note a slowing of clocks and a
shortening of rulers that are moving with respect
to the observer
  • This effect becomes significant only if the clock
    or ruler is moving at a substantial fraction of
    the speed of light

The general theory of relativity is our most
accurate description of gravitation
  • Published by Einstein in 1915, this is a theory
    of gravity
  • A massive object causes space to curve and time
    to slow down
  • These effects manifest themselves as a
    gravitational force
  • These distortions of space and time are most
    noticeable in the vicinity of large masses or
    compact objects

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  • The theory of relativity predicts a number of
    phenomena, including the bending of light by
    gravity and the gravitational redshift, whose
    existence has been confirmed by observation and

Escape Speed
  • Escape velocity is the speed an object would need
    to escape from a celestial body.
  • Gravity is low on an asteroid. You could throw a
    ball off it, or jump off it.
  • Thus, low escape velocity
  • The escape velocity depends on mass.

The general theory of relativity predicts black
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  • If a stellar corpse has a mass greater than about
    2 to 3 M?, gravitational compression will
    overwhelm any and all forms of internal pressure
  • The stellar corpse will collapse to such a high
    density that its escape speed exceeds the speed
    of light

Certain binary star systems probably
containblack holes
  • Black holes have been detected using indirect
  • Some binary star systems contain a black hole
  • In such a system, gases captured from the
    companion star by the black hole emit detectable
    X rays

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Supermassive black holes exist at the centers of
most galaxies
  • These are detected by observing the motions of
    material around the black hole

A nonrotating black hole has only a center and
a surface
  • The entire mass of a black hole is concentrated
    in an infinitely dense singularity
  • The singularity is surrounded by a surface called
    the event horizon, where the escape speed equals
    the speed of light
  • Nothingnot even lightcan escape from inside the
    event horizon

Just 3 numbers completely describe the structure
of a black hole
  • A black hole has only three physical properties
    mass, electric charge, and angular momentum
  • A rotating black hole (one with angular momentum)
    has an ergoregion around the outside of the event
  • In the ergoregion, space and time themselves are
    dragged along with the rotation of the black hole

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Falling into a black hole is an infinite voyage
  • Could a black hole somehow be connected to
    another part of spacetime, or even some other
  • General relativity predicts that such
    connections, called wormholes, can exist for
    rotating black holes

  • Mass tells space how to curve
  • Space tells mass how to move

Gravitational redshift
  • light rays (i.e. photons) lose energy as they
    climb out of a gravitational field
  • So, they shift to larger wavelength, lower energy

Gravitational Energy
  • Energy is conserved - i.e. the total energy does
    not change but it can be transferred into a
    different form
  • consider a baseball in outer space - very far
    from the Earth - we'll say infinitely far.
  • let it go from rest
  • it will reach a high velocity - and gain lots of
    energy of motion as it falls
  • energy is conserved - so where did the energy
    come from?

  • Gravity - we assign a negative potential energy
    to an object in a gravitational field
  • so, the total energy is still the same as before
  • lots of energy of motion and
  • a negative gravitational energy that compensates
    for this to allow energy conservation

  • Suppose the Earth was squeezed down to half its
    size, but kept the same mass
  • The escape velocity would be larger - 15 km/sec
    in this case
  • the baseball would slow down from 15 km/sec to 11
    km/sec by the time it reached the current radius
    of the Earth

  • Suppose the Earth was squeezed down to 1 cm
  • the escape velocity would be c
  • any smaller and its a black hole - nothing can

Sample Escapes Velocities
  • Earth 11.2 km/sec (25,000 mph)
  • Moon 2.4 km/sec
  • 1 km asteroid 1.3 m/sec
  • Sun 618 km/sec
  • White Dwarf 6000 km/sec !!

Key Words
  • black hole
  • black hole evaporation
  • equivalence principle
  • ergoregion
  • event horizon
  • general theory of relativity
  • gravitational radiation
  • gravitational waves
  • gravitational redshift
  • Heisenberg uncertainty principle
  • law of cosmic censorship
  • length contraction
  • Lorentz transformations
  • mid-mass black hole
  • no-hair theorem
  • primordial black hole
  • proper length (proper distance)
  • proper time
  • Schwarzschild radius (RSch)
  • singularity
  • spacetime
  • special theory of relativity
  • stellar-mass black hole
  • supermassive black hole
  • time dilation
  • virtual pairs
  • wormhole