L23 Blackholes
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Transcript of L23 Blackholes
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Black Holes
Formation
Spacetime
Curved spacetime Event horizon
Seeing black holes
Demo: 1L10.50 - Gravity Well - Black Hole
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A more massive neutron star has
1. A smaller radius
2. A larger radius
3. Radius is independent of mass
4. No radius
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Mass versus
radius for aneutron star
Objects too heavy
to be neutron starscollapse to black
holes
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Speed of light is constant
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Our conceptions of space and time has to
be changed.
Facts:
Regardless of speed or direction, observers always
measure the speed of light to be the same value.
Speed of light is maximum possible speed.
Consequences:
The length of an object decreases as its speed increases
Clocks passing by you run more slowly than do clocks
at rest
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Time dilation
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Time dilation
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Special Relativity: Length Contraction
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As an object speeds up, an
observer at rest would see
1. It get longer and its clock run faster
2. It get shorter and its clock run faster
3. It get longer and its clock run slower
4. It get shorter and its clock run slower
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Spacetime Diagram
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Spacetime
Diagram
Geodesic = shortest pathbetween two points.
Particles follow
geodesics in spacetime.
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Spacetime
Diagram
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If Alpha Centauri exploded 3
second ago, could there be any
effect now on Earth?
1. Yes
2. No
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Equivalence principle
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Gravitational redshift
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Precession of Mercurys orbit
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Gravity bends the path of light
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Gravity deforms space-time
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Einsteins theory of gravity is built
on the principle that1. The speed of light is constant.
2. As an object speeds up its clock runs faster.
3. The effects of gravity cannot be distinguished
from the effects of acceleration in the absence
of gravity.
4. Everyones a relative.
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Geodesics in curved spacetime
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An airplane flies from Chicago to
Beijing following the shortest
possible route
1. The path of the airplane will appear as astraight line on a normal map
2. The airplane will fly over Alaska
3. The airplane will fly over Hawaii4. The plane will fall off the end of the Earth
and never reach China
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Geodesics
in curved
spacetime
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Massive bodies and escape speed
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Gravity bends the path of light
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A nonrotating black hole has only a
center and a surface
The black hole is surrounded
by an event horizon which is
the sphere from which light
cannot escape
The distance between the
black hole and its event
horizon is the Schwarzschild
radius (RSch= 2GM/c2)
The center of the black holeis a point of infinite density
and zero volume, called a
singularity
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Event horizon
Th l l d ib h
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Mass As measured by the
black holes effect on
orbiting bodies, such asanother star
Total electric charge
As measured by thestrength of the electricforce
Spin = angular momentum
How fast the black holeis spinning
Three parameters completely describe thestructure of a black hole
Most properties of mattervanish when matter enters
a black hole, such aschemical composition,texture, color, shape, size,distinctions betweenprotons and electrons, etc
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Rotating black holes
A rotating black hole(one with angularmomentum) has anergosphere around theoutside of the eventhorizon
In the ergosphere, spaceand time themselves are
dragged along with therotation of the blackhole
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Falling into a black hole
Falling into a black hole gravitational tidal forces pull
spacetime in such a way that time becomes infinitely long
(as viewed by distant observer). The falling observer seesordinary free fall in a finite time.
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Falling into a black holes
With a sufficiently large black hole, a freely fallingobserver would pass right through the event horizon
in a finite time, would be not feel the event horizon.
A distant observer watching the freely falling
observer would never see her fall through the eventhorizon (takes an infinite time).
Falling into smaller black hole, the freely falling
observer would be ripped apart by tidal effects.
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Falling into a black hole
Signals sent from the freely falling observer would betime dilated and redshifted.
Once inside the event horizon, no communication with
the universe outside the event horizon is possible. But incoming signals from external world can enter.
A black hole of mass M has exactly the same
gravitational field as an ordinary mass M at large
distances.
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As you fall into to a black hole, you shine a
blue flashlight at a friend exterior to the
hole, she sees
1. blue light2. blue light at first, then turning red
3. blue light, then red, then nothing
4. nothing
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Seeing black holes
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Seeing black holes
Bl k h l
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Black holes evaporate
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Review Questions
1. What are the two facts which caused Einstein to invent
the special theory of relativity?
2. What are two key consequences of special relativity for
how we observe moving objects?
3. What effect does gravity have on spacetime?4. How do astronomers search for black holes?
5. In what sense is a black hole black?
6. How are black holes actually simpler than any otherobjects in astronomy?
7. What happens to an object that falls into a black hole?
8. Do black holes last forever?