General Theory of Relativity (1916)

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General Theory of Relativity (1916)
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Can an experiment tell us if we are in a moving
train or on the platform of the station?
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The ball dropped from the top of the mast reaches
the bottom of the mast
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The laws of physics are the same on the boat and
on a cliff, as long as the boat has a constant
speed and moves in a straight line
The laws of physics are the same in the train and
on the ground, as long as the train has a
constant speed and moves in a straight line
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What if the vehicle is accelerating?
Or decelerating?
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Can an experiment tell us if we are in an
accelerating train or on the platform of the
station?
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Pendulum
Accelerating train
Train at rest
Decelerating train
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Galileo was interested in vehicles moving at
constant speed. What does physics look like on
board an accelerating rocket?
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Closed box
Empty space (no planet, star or galaxy around)
Zero-gravity
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Add a planet
gravitation
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Instead add thrusters and accelerate
acceleration
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What experiment on board the rocket could make
the difference between these two situations?
acceleration
gravitation
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Equivalence principle There is no way to tell
locally the different between acceleration and
gravity.
No experiment can make the difference!
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d2
d2
d1
d1
Gravity bends light!
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How can photons be attracted by a gravitational
field they have no mass!
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Photons are still following a straight line
path, but space-time is curved by massive objects
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The presence of mass curves space-time
energy
2D space-time
Space-time a "rubber sheet" that is usually
flat but when a mass is placed on this "rubber
sheet", it stretches and curves in response
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• The flatland or rubber 2D space-time does not
  make much sense...
• Here are more telling representations

http//www.youtube.com/watch?vDbhuRcmSkMgfeature
related
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When space-time is curved, a moving object must
follow the curvature, i.e. change its speed and
direction, just as a car must turn when the
highway curves.
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Consequence we can see a star that is behind the
Sun
Verified during the solar eclipse of 1919, when a
star that should have been invisible behind the
eclipsed Sun could be seen.
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The presence of mass slows down time Clocks run
more slowly near a massive object another form
of time dilation                      
faster
MASS
slower
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Atomic clocks can detect a time difference
between the bottom and top of a tall building!
faster
Closer to the Earth
slower
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Which clock is ticking slower?
A clock on the Earth or a clock on the Moon?
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Moon
Earth
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Newton's Laws are approximations to General
Relativity that are only applicable away from
large masses. General Relativity is a
generalization of Newton's Laws of Motion and
Gravitation.
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In practice, one must have an escape velocity
faster than 0.1c to observe these relativistic
effects.Nevertheless, with sensitive
experimental equipment, the predictions of
General Relativity have been verified to high
precision
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At the end of his paper Einstein wrote
Anyone who understands the present theory could
not miss its magic.
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The main appeal of this theory lies in the fact
that it is self-contained. Should any of its
conclusions be invalidated, the entire theory
would have to be rejected. It is impossible to
modify it without jeopardizing the entire
structure.
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Pratice
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1. Which statement best describes the fabric of space and time as outlined by the classical physics of Newton?
A) Space is expanding uniformly, while time passes more slowly as the universe ages.
B) Space becomes curved and time slows down near a source of gravity, as measured by a distant observer.
C) The shape of space and the rate of passage of time depend upon the relative velocities of observer and observed.
D) Space is perfectly uniform, filling everywhere like a fixed network, while time passes at a uniform rate for all observers.
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B
A
C
D
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2. At which of the following locations will Newton's laws of motion be inadequate in describing precisely the motions of objects?
A) In the Space Shuttle, moving around the Earth at a speed of about 8 km/sec.
B) At the center of the Earth.
C) Inside an artillery shell as it accelerates inside the gun barrel.
D) Inside the orbit of Mercury.
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2. At which of the following locations will Newton's laws of motion be inadequate in describing precisely the motions of objects?
A) In the Space Shuttle, moving around the Earth at a speed of about 8 km/sec. NOT FAST ENOUGH
B) At the center of the Earth. NO GRAVIT. PULL
C) Inside an artillery shell as it accelerates inside the gun barrel. NOT FAST ENOUGH
D) Inside the orbit of Mercury. GRAVITATIONAL PULL OF THE SUN
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B
A
C
D
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3. In what way is the general theory more general (i.e., deals with more situations) than the special theory of relativity?
A) It includes gravitation and accelerated motion.
B) It includes the change in the rate of passage of time when objects are in motion.
C) It includes motion at and above the speed of light.
D) It includes only constant, unaccelerated motion.
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B
A
C
D
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4. How does a gravitational field affect the passage of time?
A) Gravity has no effect on the passage of time.
B) Clocks in a gravitational field run slower than clocks outside the field.
C) Gravity makes time stop.
D) Clocks in a gravitational field run faster than clocks outside the field.
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B
A
C
D
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5. In which of the following locations would a clock run at its fastest rate?
A) In empty space.
B) On the Earth's surface.
C) In the Jupiter atmosphere.
D) In the weightless environment on the Space Shuttle in orbit around the Earth.
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B
A
C
D
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6. Suppose you were far from a planet that had a very strong gravitational field, and you were watching a clock on the surface of the planet. During the time in which your own clock ticks out a time of 1 hour, how much time does the clock on the planet tick out?
A) Less than 1 hour (but more than zero).
B) No time at all.
C) More than 1 hour.
D) Exactly 1 hour, the same as yours.
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B
A
C
D
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7. According to Einstein's theory of general relativity, if you watch a clock from a distant location as it is moved closer to a source of gravity, you will see the clock
A) maintain the same rate, since time is unaffected by gravity.
B) only change its rate if it is moving rapidly, but maintain its standard rate if stationary in a gravity field.
C) slow down.
D) run faster.
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B
A
C
D
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8. According to Newton's law of gravity, why does the Earth orbit the Sun?
A) The Sun exerts a gravitational force on the Earth across empty space.
B) The Earth and the Sun are continually exchanging photons of light in a way that holds the Earth in orbit.
C) Matter contains quarks, and the Earth and Sun attract each other with the color force between their quarks.
D) Space around the Sun is curved.
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B
A
C
D
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9. According to general relativity, why does the Earth orbit the Sun?
A) Matter contains quarks, and the Earth and Sun attract each other with the color force between their quarks.
B) Space around the Sun is curved.
C) The Sun exerts a gravitational force on the Earth across empty space.
D) The Earth and the Sun are continually exchanging photons of light in a way that holds the Earth in orbit.
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B
A
C
D
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10. Which of the following is not a test of general relativity, but rather is a test of special relativity?
A) The length of a moving object decreases when observed by a stationary observer.
B) The wavelength of light increases as it leaves a region of gravitational field.
C) Light travels in a curved path in a gravitational field.
D) The perihelion position of Mercury's orbit precesses more quickly than is predicted by Newtonian theory.
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B
A
C
D
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Gravitational redshift
Space-time affects the behaviour of light
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Photons leaving a star lose energy in climbing
out the stars gravitational field they become
redder
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Example photons leaving a black hole
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Black Holes
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Escape Velocity The minimum speed necessary to
move away from a massive body and never return.
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If the escape velocity is greater than the speed
of light , then even light cannot escape from the
source of gravity.
The object appears black against the background
of the stars
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Light escaping a massive object
Neutron star
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Light trapped into a black hole
Event horizon
Schwarzschild radius
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The event horizon is not the surface of the black
hole but the surface where the escape velocity
becomes equal to the speed of light
Structure of a non-rotating black hole
(orSchwarzschild black hole)
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A black hole is an object of zero extent which
contains all the mass of the collapsed object.
It is a singularity, a mathematical point of
infinite density and gravity.
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Schwarzschild radius in km 3 x mass of the
black hole in solar masses
Mass (Mo) Schwartzschild radius
Massive star 10
Sun 1
Earth 0.000003
30km
3 km
0.9 cm
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• The three main effects of a black hole are
• Tidal forces
• Gravitational redshift
• Gravitational time dilation
• .

Tidal forces acting on an astronaut
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Gravitational redshift(Spinning black hole)
Can spin thousands of time per second
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Travelling into a black hole
To Calvin, the clock of the rest of the universe
runs faster and faster. Calvin can see the
fate of the universe!
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To Calvin, photons coming from the universe gain
more and more energy. They look more and more
blue, then UV, then he receives only X-rays, then
gamma rays. But gamma rays are very hard detect!
Will Calvin die first from being a spaghetti
(tidal stretch) or from being cooked (by
gamma-rays)?
We don't know...
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To Hobbes, Calvin becomes redder and redder, and
finally Hobbes sees a radio image of Calvin
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To Hobbes, Calvin seems to slow down as he
approaches the event horizon. Calvins speed
comes closer and closer to zero. Calvins heart
beat seems to slow down to. Calvin never crosses
the event horizon.
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After crossing the event horizon

• Times becomes space, space becomes time. One
  cannot control one's motion, but one can control
  one's time )
• One cannot see anything below, not even one's
  feet below black/dark.
• Above intense soup of gamma-rays.

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The Search for Black Holes

• Black holes do not have a magnetic field.
• All we can know about a black hole is
• its mass,
• its angular momentum,
• its electrical charge.
• Although black holes emit no light, we can hope
  to detect them by means of their strong
  gravitational influence on nearby matter.

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An X-ray binary system may contain a black hole
if the mass of the compact object is too great
for it to be a neutron star (more than 3 Mo)
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The gas waiting to fall forms an accretion disk
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When material falls into a black hole, it gets
heated to millions of degrees and accelerated.
The superheated materials emit X-rays, which can
be detected by X-ray telescopes such as the
orbiting Chandra X-ray Observatory
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The star Cygnus X-1 is a strong X-ray source.
Stellar winds from the companion star, HDE
226868, blow material onto the accretion disk
surrounding the black hole.
X-ray image of Cygnus X-1 taken from orbiting
Chandra X-ray Observatory
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Black holes can also eject materials at high
speeds to form jets. Many galaxies have been
observed with such jets they have supermassive
black holes (billions of solar masses) at their
centers. They emits powerful radio waves.
Schematic diagram of active galactic nucleus
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The images on the left and bottom are radio
images of the heart of galaxy M87. The image on
the right is a visible image from the HST. Note
the jet of material coming from M87.
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Quasars

• The brightest type of active galactic nucleus
• Believed to be powered by a supermassive black
  hole
• Thousands of quasars have been observed, all at
  extreme distance from our galaxy

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Quasar
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You have been selected for a space mission that
will confirm the existence of black holes
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Only those who will obtain an odd mark will go on
board the space ship (Scouts)
Those who obtain an even mark (Reporters) will
stay on Earth to follow the mission on a TV
screen.
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Pre-test 24 questions
Good luck!
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1. Black holes are so named because
A) no light or any other electromagnetic radiation can escape from inside them.
B) all of their electromagnetic radiation is gravitationally redshifted to the infrared, leaving no light in the optical region.
C) they emit a perfect blackbody spectrum.
D) their only emissions are in the radio and the infrared, with no visible radiation.
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2. The escape velocity for material behind the event horizon The escape velocity for material behind the event horizon
A) A) zero.
B) B) infinite.
C) C) greater than the speed of light.
D) D) twice that from a neutron star.
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3. Light leaving the surface of a neutron star is strongly redshifted. What name is given to this effect?
A) Cosmological redshift.
B) Gravitational redshift.
C) Zeeman effect.
D) Doppler shift.
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4. If the Sun were replaced by a 1-solar-mass black hole, then the Earth would
A) enter an elliptical orbit passing close to the black hole, with its furthest distance from the black hole equal to 1 AU.
B) spiral quickly into the black hole.
C) head off into interstellar space along a straight line tangent to its original orbit around the Sun.
D) continue to orbit the black hole in precisely its present orbit.
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5. A black hole can be thought of as
A) a star with a temperature of 0 K, emitting no light.
B) the point at the center of every star, providing the star's energy by gravitational collapse.
C) strongly curved space.

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6. Which effects have been useful (and successful) in the search for and identification of black holes in the universe?
A) The influence of their intense gravitational field on atoms that are emitting light from the event horizons of the black holes.
B) Their gravitational influence on nearby matter, particularly companion stars.
C) The effect of their angular momentum or spin on nearby matter.
D) Their magnetic fields and the influence on these fields upon nearby matter.
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7. What mechanism in the vicinity of a star gives us a hint of the presence of a black hole as a companion to the star?
A) The light from the companion star shows extreme redshift because of the gravitational field of the black hole.
B) The periodic disappearance of the star from the viewpoint of Earth during its eclipses by the black hole as these two objects orbit each other.
C) The darkening of the space near the star, indicating that the black hole prevents the light from distant objects from reaching the Earth.
D) Gas from the star, falling in toward a black hole, is compressed to very high densities and temperatures so that it emits an intense and rapidly fluctuating flux of X rays.
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8. I always thought nothing could escape from a black hole, yet astronomers are locating black hole candidates by the X rays they emit. How can X rays be coming from a black hole?
A) The X rays come from a highly compressed region in an accretion disk outside the event horizon of the black hole.
B) X rays are not light or matter and can therefore escape from inside the black hole.
C) If the black hole is rotating, it modifies spacetime around it so much that particles and X rays are created in the vacuum just outside the event horizon.
D) The X rays are produced by vibrations of the black hole itself, and therefore do not come from inside the black hole.
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9. 9. Where would you look for a supermassive black hole?
A) In the center of a galaxy. In the center of a galaxy.
B) At the center of the universe. At the center of the universe.
C) Orbiting a normal star in our Galaxy. Orbiting a normal star in our Galaxy.
D) At the center of a supernova remnant. At the center of a supernova remnant.
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10. 10. What name is given to any black hole that might have been created in the Big Bang at the beginning of the universe?
A) A supermassive black hole. A supermassive black hole.
B) A Schwarzschild black hole. A Schwarzschild black hole.
C) A Kerr black hole. A Kerr black hole.
D) A primordial black hole. A primordial black hole.
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11. What separates a black hole from the rest of the universe?
A) Its crystalline crust.
B) The surface of the ergosphere.
C) Its singularity.
D) Its event horizon.
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12. What is the event horizon of a black hole?
A) The surface at which any object passing through it will leave with greater energy than it entered.
B) The surface at which all events happen.
C) The infinitesimally small volume at the center of the black hole that contains all of the black hole's mass.
D) The surface from inside of which nothing can escape.
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13. 13. At what location in the space around a black hole does the escape velocity become equal to the speed of light?
A) At the point where clocks are observed to slow down by a factor of 2. At the point where clocks are observed to slow down by a factor of 2.
B) Only at the central singularity. Only at the central singularity.
C) At the event horizon. At the event horizon.
D) At the point where escaping X rays are produced. At the point where escaping X rays are produced.
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14. Where is the event horizon of a black hole located?
A) At the position of maximum X-ray emission.
B) At the singularity.
C) At the outer surface of the ergoregion.
D) At the Schwarzschild radius away from its center.
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15 What is it that is actually located at the event horizon of a black hole?
A) An infinitely dense concentration of mass.
B) A magnetic field of immense strength.
C) Nothing specific.
D) A sphere of photons.
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16. What is a singularity?
A) A particle-antiparticle pair.
B) A tunnel into another universe.
C) Any point at the Schwarzschild radius of a black hole.
D) A point of infinite density.
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17. What is the Schwarzschild radius of a 2-solar-mass black hole?
A) 60 km.
B) 6000 km.
C) 6 m.
D) 6 km.
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18. 18. Which of the following can you never know about a black hole?
A) The type of material inside it. The type of material inside it.
B) Its angular momentum (spin). Its angular momentum (spin).
C) The total amount of matter (the mass) inside it. The total amount of matter (the mass) inside it.
D) Its net electric charge. Its net electric charge.
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19. What happens to the magnetic field of a star that collapses to become a black hole?
A) The magnetic field becomes infinitely intensified.
B) The magnetic field is radiated away black holes never have magnetic fields.
C) The magnetic field becomes compressed and intensified by a factor equal to the ratio of the star's original diameter to the diameter of the event horizon.
D) The magnetic field becomes weaker by the ratio of the diameter of the black hole event horizon to the star's original diameter.
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20. What is a Schwarzschild black hole?
A) A supermassive black hole.
B) Any uncharged black hole.
C) A black hole that fills its Schwarzschild radius with matter.
D) A regular, non rotating, black hole.
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21. What name is given to a rotating black hole?
A) A Schwarzschild black hole.
B) A Hawking singularity.
C) A wormhole.
D) A Kerr black hole.
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22. A space freighter accidentally drops a steel beam while passing a black hole, and the beam starts falling toward the black hole with the long direction of the beam pointing toward the black hole. What happens to the beam as it approaches the event horizon?
A) It expands in all dimensions to the size of the black hole event horizon when it reaches this distance from the singularity.
B) It is stretched in length and compressed in width.
C) It is compressed in both length and width.
D) It is compressed in length and stretched in width.
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23. Suppose it were possible to lower a yellow sodium lamp down toward the event horizon of a black hole. What would you see while watching from a safe distance?
A) The brightness or color would each remain unchanged.
B) The light from the lamp would change to orange then red.
C) The light would remain yellow, but there would be less and less photons being emitted from it.
D) The light from the lamp would change to green then blue.
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24. 24. What appears to happen to a clock as it approaches and reaches the event horizon around a black hole, when viewed by a remote observer?
A) Time appears to pass at a much faster rate, this rate becoming infinitely fast at the event horizon. Time appears to pass at a much faster rate, this rate becoming infinitely fast at the event horizon.
B) It appears to slow down and stop. It appears to slow down and stop.
C) It speeds up because of the intensified gravitational field. It speeds up because of the intensified gravitational field.
D) It ticks uniformly, since nothing changes the progress of time. It ticks uniformly, since nothing changes the progress of time.
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Ask your neighbour to mark your pre-test
1A 2C 3B 4D 5C 6B
7D 8A 9A 10D 11D 12D
13C 14D 15C 16D 17D 18A
19B 20D 21D 22B 23B 24B