일반 상대성 이론 퀴즈

9주

 1. In the Schwarzschild spacetime, two events happen at the same position but at slightly different time. The events happen near the Schwarzschild radius.

Then the proper time difference of two events is the same as the coordinate time difference.

True or False?

Answer : 슈바르츠실트 반지름에 가까워지면 블랙홀에 가까워 지는 상태가 된다. 즉 슈바르츠실트 반지름보다 작아지면 (지구의 경우 반지름이 9mm가 될 경우) 중력의 힘이 너무 강해져 물체는 계속해서 수축하는 상태가 된다. 

proper time은 특수상대성 이론에서 관측자와 물체가 동일한 속도로 이동하고 있을 때, 즉 관측자와 물체와의 상대적인 속도 차이가 존재하지 않을 때 관측자가 측정한 물체의 시간이다.

coordinate time 은 

proper time difference는 coordinate time difference와 다르다.

2. A light wave of  was produced at the surface of a star 10 milion light years away. The radius of the star is . When the light arrives on the Earth, what is its frequency?

Select one:

1. 

2. 

3. 

4. 

The correct answer is: 

3.In the Schwarzschild spacetime, two events happen at the time and at the same angles. The events happen near the Schwarzschild radius.

The proper distance betweem two events is larger than the radial distance.

Select one:

True

False

The correct answer is 'True'.

On a geodesic curve, there is a point when a tangent vector is not parallel to itself under parallel transport.

Select one:

True

False

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The correct answer is 'False'.

A test particle falls freely in a Schwarzschild spacetime. The size of its angular momentum per unit mass is conserved. 

Select one:

True

False

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The correct answer is 'True'.

Find the correct expression for the effective potential in a Scwarzshild spacetime.

Select one:

1. 

2. 

3. 

4. 

Feedback

The correct answer is: 

In a Schwarzschild spacetime, the elliptic orbit of a test particle around a mass may precess, due to an extra term in the effective potential.

Select one:

True

False

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The correct answer is 'True'.

10주

A black hole is an area of space time where matter and radiation may enter, but from which they may not escape.

Select one:

True

False

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The correct answer is 'True'.

An event horizon is a name for a surface which traps red lights but not blue lights. An event horizon bounds a black hole.

Select one:

True

False

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The correct answer is 'False'.

For a white dwarf, the Chandrasekhar limit is 3 times the solar mass.

Select one:

True

False

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The correct answer is 'False'.

A black hole which does not rotate is discrebed by the Kerr metric.

Select one:

True

False

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The correct answer is 'False'.

The mass of a supermassive black hole is usually 105  to 1010 times the solar mass.

Select one:

True

False

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The correct answer is 'True'.

Let's say an observer is staying at the surface of a gravitationally collapsing star, which eventually became a black hole. For the observer, it took an infinitely long time to pass the event horizon.

Select one:

True

False

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The correct answer is 'False'.

An observer on the Earth is watching a far away star becomes a black hole. For the observer, it takes infinitely long time for the star to collapse gravitationally.

Select one:

True

False

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The correct answer is 'True'.

For an astronaut falling freely around the Schwarzschild radius of a supermassive black hole whose mass is 107 times the solar mass, the gravitational field gradient is negligible.

Select one:

True

False

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The correct answer is 'True'.

11주

Under a certain condition, a photon emitted between the event horizon and the photon sphere to the outward direction from a non-rotating black hole can escape the photon sphere.

Select one:

True

False

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The correct answer is 'True'.

A muon particle is falling down to a non-rotating black hole. We use the Schwarzschild coordindate system to describe the path of the muon.  The light cone of the muon becomes narrower and tilting more toward the central singularity smoothly when the muon passes beyond the event horizon.

Select one:

True

False

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The correct answer is 'False'.

The advanced Eddinton Finkelstein coordinate system has two singularities: one is physical and the other is a  coordinate singularity.

Select one:

True

False

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The correct answer is 'False'.

It's highly likely that a black hole has non-zero angular momentum.

Select one:

True

False

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The correct answer is 'True'.

The physical sigularity of a Kerr black hole with non-zero angular momentum is not a point.

Select one:

True

False

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The correct answer is 'True'.

According to the Penrose process, a rotating black hole cannot lose energy or angular momentum at any circumstances.

Select one:

True

False

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The correct answer is 'False'