일반상대성 이론 퀴즈 2

14주

When the curvature parameter of a universe k equals +1, its hypersurface is closed and bounded.

Select one:

True

False

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The correct answer is 'False'.

When the curvature parameter of a Universe k equals 0, both the 3D hypersurface and the 4D Robertson-Walker metric of the Universe are flat.

Select one:

True

False

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The correct answer is 'False'.

The curvature parameter k decribes the curvature of the 3D hypersurface of the Universe. Find the correct statement for each k case.

The sum of the internal angles of a triangle is 180 degrees.	Answer 1Choose...k = -1k = +1k = 0
The sum of the internal angles of a triangle is less than 180 degrees.	Answer 2Choose...k = -1k = +1k = 0
The sum of the internal angles of a triangle is larger than 180 degrees.	Answer 3Choose...k = -1k = +1k = 0

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The correct answer is: The sum of the internal angles of a triangle is 180 degrees. – k = 0, The sum of the internal angles of a triangle is less than 180 degrees. – k = -1, The sum of the internal angles of a triangle is larger than 180 degrees. – k = +1

The recent data sets on CMBR support the statement that the Universe is homogeneous and isotropic.

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True

False

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The correct answer is 'True'.

The cosmological principle is as follows: At any given time, and on a sufficiently large scale, the Universe is homogeneous and anisotropic.

Select one:

True

False

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The correct answer is 'False'.

The dark energy cannot be the energy of vaccum. Since the predicted density of vaccum energy is too large for the estimated density of dark energy.

Select one:

True

False

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The correct answer is 'True'.

Find all the principles which are the basis for modern cosmology.

Select one or more:

1. The Robertson-Walker metric is used to descibe the spacetime.

2. The energy-momentum tensor consists of mater, radiation, and dark energy.

3. The evolution of the Universe is described by the Friedmann equation(s).

4. The spacetime of our Universe is closed.

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The correct answer is: The Robertson-Walker metric is used to descibe the spacetime., The energy-momentum tensor consists of mater, radiation, and dark energy., The evolution of the Universe is described by the Friedmann equation(s).

13주

 Black holes – Mini black holes – Stella mass black holes – Intermediate mass black holes – Supermassive black holes

Binary Stars with X-ray Emission,Cygnus X-1 and HDE 226868,Cygnus X-1 with Event Horizon?,Intermediate Mass Black Holes (IMBH),IMBH Candidate: GW190521,Supermassive Black Holes (SMBH)

• There is a good evidence that stella mass black holes, IMBH, and SMBH exist. • It is believed that many galaxies including our own Milky way have SMBH at their centers. • The rotation of black holes has been proved by indirect analysis such as distortion in the x-ray spectrum. • Hubble Space Telescope observed two pulse trains fell behind the event horizon. • The strong luminosity of quasars can be explained by gravitational energy release via accretion onto black holes. • The extragalactic X-ray sky is dominated by such gravitationally powered sources.

Gravitational lensing

Gravitational Lensing • There are many examples of gravitational lensing effects. • Micro-gravitational lensing can be used to find exo-planets

• Gravitational waves and Einstein field equations • Methods of detecting gravitational waves • Sources of gravitational waves

Pulsar

• Gravitational waves are a product of Einstein’s field equation. – It is a linearized version of a weak gravitational field. • Since 2015, LIGO and VIRGO experiments have recorded GW observations successfully. • With the detection of GW signals, the field of multi-messenger astronomy became more active than ever. This astronomy strategy consists of – Electromagnetic radiations over a broad spectrum of optical telescopes (radio, visible, x-rays) – Gravitational waves, – Neutrinos, and – Cosmic rays

12주

Gravity Probe B is a satellite experiment to test several predictions of general relativity. Find all of these tests in the given choices.

Select one or more:

1. Geodesic gyroscope precession

2. Frame dragging

3. Gravitational redshift

4. Deflection of light by the Sun

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The correct answer is: Geodesic gyroscope precession, Frame dragging

A satellite was sent to a low polar orbit. At the start of the experiment, the spin axis of a gyroscope in the satellite was pointing radially to the outside of the Earth. What is the precession angle of the axis due to the geodesic gyroscope precession effect? Find the closed number.

Select one:

1. 0.08 arcsecond per year

2. 0.8 arcsecond per year

3. 8 arcsecond per year

4. 80 arcsecond per year

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The correct answer is: 8 arcsecond per year

NASA tested the Shapiro time delay with the Voyagers spacecrafts. However, the accuracy was always worse than 10%. NASA concluded they cannot use the Shapion time delay with the Voyagers.

Select one:

True

False

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The correct answer is 'False'.

The gravity field at the orbits of the GPS satellites is weaker than the gravity field on the ground. Therefore, an adjustment should be applied continuously to correct the atomic clock in each satellite. Otherwise, the position information by the GPS would be off at the rate of tens of kilometers per day.

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True

False

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The correct answer is 'True'.

In 1964, Pound and Rebka tried to measure the redshift caused by the Earth at a laboratory at Harvard University, but their result was inconclusive.

Select one:

True

False

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The correct answer is 'False'.

VLBI (Very long baseline interferometers) can observe the deflection of light by the Sun with an accuracy better than 0.04%.

Select one:

True

False

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The correct answer is 'True'.

What is the general relativity (Schwartzschild metric) contribution to the precession of the perihelion of the Mercury per century? Find the closest value.

Select one:

1. -0.002 arcsec

2. 0.0286 arcse

3. 43 arcsec

4. 532 arcsec

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The correct answer is: 43 arcsec

9주

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'.

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

Select one:

1. 

2. 

3. 

4. 

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The correct answer is: 

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'.

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'.

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

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The correct answer is 'True'.

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. 

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The correct answer is: 

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.

Select one:

True

False

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The correct answer is 'False'.

10주

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.

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True

False

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The correct answer is 'True'.

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'.

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'.

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'.

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'.

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'.

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'.

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'.

 11주 

The value of Planck energy is . This is an extremely small value.

Select one:

True

False

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The correct answer is 'False'.

If true, the Hawking radiation can make a black hole evaporate, since the black hole can consume all of its mass by emitting radiation.

Select one:

True

False

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The correct answer is 'True'.

If true, the Hawking radiation makes it possible for a black hole to emit a postive energy particle, which can be observed by a distant observer.

Select one:

True

False

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The correct answer is 'True'.

Due to quantum fluctuation, a pair of virtual particles can be created in a vaccum for a long time, as long as their energy is deteremined under the condition.

Select one:

True

False

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The correct answer is 'False'.

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'.

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

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True

False

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The correct answer is 'True'.

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

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True

False

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The correct answer is 'True'.

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'.

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'.

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'.