L23 Blackholes

8/3/2019 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?

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L23 Blackholes