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## Black Holes

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### 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

1
Black Holes
2
Newtonian
• Universal Mutual Gravitation Isaac Newton, in his
Principia, formulated the Law of Universal Mutual
Gravitation
• 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

3
• 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.

4
• 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"

5
• 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"

6
The Flaw
• Doesnt work when you are talking about intense
gravitational force of black holes and neutron
stars
• Thankfully Einstein created the principles of
relativity

7
• In Newtonian gravitation, an orbit is always an
ellipse.
• 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
light,

8
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
time.
• 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.

11
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.

12
The special theory of relativity changes our
conceptions of space and time
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
spacetime

13
Special Relativity
• General Relativity developed from Special
Relativity
• 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
mph)
• We see the ball move at vtrainvball 70 m/sec
(160 mph) from the ground

14
• 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
km/sec!
• Even if the train moved at vtrain 200,000
km/sec, we'd still see the light move at velocity
c!

15
• 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

16
The speed of light is the same to all observers,
no matter how fast they are moving
17
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

18
The general theory of relativity is our most
accurate description of gravitation
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
experiment

21
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.

22
The general theory of relativity predicts black
holes
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26
• 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

27
Certain binary star systems probably
containblack holes
• Black holes have been detected using indirect
methods
• 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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31
Supermassive black holes exist at the centers of
most galaxies
• These are detected by observing the motions of
material around the black hole

32
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

33
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
horizon
• In the ergoregion, space and time themselves are
dragged along with the rotation of the black hole

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35
Falling into a black hole is an infinite voyage
36
• Could a black hole somehow be connected to
another part of spacetime, or even some other
universe?
• General relativity predicts that such
connections, called wormholes, can exist for
rotating black holes

37
• Mass tells space how to curve
• Space tells mass how to move

38
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

39
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?

40
• 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

41
• 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

42
• Suppose the Earth was squeezed down to 1 cm
• the escape velocity would be c
• any smaller and its a black hole - nothing can
escape!

43
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 !!

44
Key Words
• black hole
• black hole evaporation
• equivalence principle
• ergoregion
• event horizon
• general theory of relativity
• 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