Spring 2019 ASTR 3740 Clicker Questions

Spring 2019 ASTR 3740 Homepage

Spring 2019 ASTR 3740 Black Holes: Clicker Questions

Mon 2019 Jan 14 (not graded):

Will you get an A in this class?
A. Yes, I am at least 90% sure of it.
B. I think I have a better than 50% chance.
C. Probably not.
In this class, I am most interested in learning about:
A. Relativity.
B. Black Holes.
C. Cosmology.
D. All of the above.
E. Something else.
Wed 2019 Jan 16 (not graded):
Which of the following is an inertial frame?
A. The frame of an object in free-fall.
B. The frame of an object at rest in this room.
C. The frame of a person on a roller coaster.
D. The frame of an electron in an atom.
E. All of the above.
Which conservation law is the odd-person-out?
A. Conservation of energy.
B. Conservation of momentum.
C. Conservation of angular momentum.
D. Conservation of velocity of center of mass.
E. Conservation of electric charge.
Fri 2019 Jan 18:
If the postulates of special relativity are correct, would the light have moved differently if Cerulean, not Vermilion, had emitted the light?
A. Yes.
B. No.
In special relativity, reality depends on the observer, and it is possible for two logically inconsistent things to occur.
A. True.
B. False.
Wed 2019 Jan 23:
Why is the wavelike nature of light difficult to see?
Two circular hoops of the same size start at rest. Hoop A starts moving at near the speed of light towards hoop B. Which hoop passes inside the other?
A. A.
B. B.
C. Neither.
Fri 2019 Jan 25:
Most of the apparent paradoxes of special relativity arise because?
If Cerulean were moving as shown relative to Vermilion, which line would be a “now line” for Cerulean?
A.
B.
C.
D.
E.

Mon 2019 Jan 28:
On your way out to Alpha Cen, you appear to me, watching you through a telescope on Earth, to move at what speed?
A. 0;
B. ½ c;
C. Near c;
D. 2 c;
E. Near infinite speed.
On your way back from Alpha Cen, you appear to me, watching you through a telescope on Earth, to move at what speed?
A. 0;
B. ½ c;
C. Near c;
D. 2 c;
E. Near infinite speed.
If round-trip time is 8 years from my (Earth) perspective, then the round-trip time from your (traveler's) perspective is:
A. less than 8 years;
B. 8 years;
C. more than 8 years.
Will the spaceship fit inside the space station?
A. Yes.
B. No.
Mon 2019 Feb 4:
On a spacetime diagram, the worldline of a person must point:
A. vertically upward;
B. at less than 45° from vertical;
C. at 45° from vertical;
D. horizontally;
E. in any direction.
How does the rest mass m of a spacecraft change with its velocity v?
A. It increases.
B. It stays the same.
C. It decreases.
Wed 2019 Feb 6:
In the twin paradox, you and your twin start at the same place, recede from each other at some velocity, then return at the same velocity. The situation seems symmetrical. What breaks the symmetry, that allows the twin to be younger than you on return?
A. The velocities at which you and your twin see each other move are different.
B. The situation is in fact symmetrical, so in fact you must both age the same.
C. The twin moves through space, whereas you do not.
D. The twin accelerates at the turnaround point, whereas you do not accelerate.
E. The twin experiences a sudden loss of time at the turnaround point.
Your twin watches you on Earth through a telescope. At the moment that the twin accelerates at Alpha, the twin sees your clock:
A. Run at the same slowed-down rate both before and after accelerating.
B. Suddenly change from 2 years to 8 years.
C. Suddenly speed up.
D. Suddenly slow down.
E. Change from running forward to runing backward.
You pass through a scene at near the speed of light. Clocks on objects ahead of you appear speeded by exactly the same amount as the frequencies of photons of light from those objects appear increased. True or false?
A. True.
B. False.
In George Gamow's classic book “Mr. Tomkins in Wonderland,” Mr. Tomkins has a dream that the speed of light is 30mph. In the dream, passing bicyclists appear Lorentz contracted along the direction of their motion. Does Mr. Tomkins' dream portray correctly the appearance of objects moving relativistically?
A. Yes.
B. No.
Mon 2019 Feb 18:
Suppose you watch this scene while falling freely. According to the Principle of Equivalence, what kind of trajectory will the cannonball follow from your perspective (relative to you)?
A. A vertical line.
B. A straight line.
C. A curved (parabolic) line.
Standing on the surface of the Earth, you hold a negative mass object in your hand. According to the Principle of Equivalence, which way does the negative mass object fall when you drop it?
A. Down to the floor;
B. It justs hangs there in mid-air, falling neither down nor up;
C. Up to the ceiling;
D. None of the above.
You are in flat space. You swing a clock on a rope in a circle around you, so that the clock is moving at near the speed of light relative to you. According to Special Relativity, the clock will appear to you to tick:
A. Slow;
B. At the same rate as your own clock;
C. Fast;
D. None of the above.
Wed 2019 Feb 20:
In the situation of the previous question, the object therefore appears to you (according to Special Relativity):
A. Redshifted;
B. Neither redshifted nor blueshifted;
C. Blueshifted.
According to Special Relativity, does B see the light from A to be redshifted or blueshifted?
A. B sees the light to be redshifted (lower energy) compared to A.
B. B sees the light to have the same energy as A.
C. B sees the light to be blueshifted (higher energy) compared to A.
On this map, the shortest distance between Boulder (40^oN 105.25^oW) and Dushanbe, Tajikstan (38.5^oN 68.75^oE) over the Earth's surface is:
A. A straight line;
B. A curved line.
Fri 2019 Feb 22:
In general, does the metric \(g_{ij}\) have to be diagonal (\(g_{ij} \neq 0\) only if \(i = j\))?
A. Yes.
B. No.
In general, does the metric have to be symmetric (\(g_{ij} = g_{ji}\))?
A. Yes.
B. No.
Mon 2019 Feb 25:
How do you know that a spacetime is globally curved (not flat)?
A. In free fall, all spacetimes are globally flat.
B. Geodesics are straight lines.
C. Geodesics that are initially parallel remain parallel.
D. The spacetime is embedded in a higher dimensional spacetime.
Can spacetime be curved inside a region where there is no mass?
A. Yes.
B. No.
Wed 2019 Feb 27:
The Schwarzschild metric is \[ d s^2 = - ( 1 - r_s/r ) \, dt^2 + {dr^2 \over 1 - r_s/r} + r^2 ( d\theta^2 + \sin^2\!\theta \, d\phi^2 ) \] where \(r_s = 2 G M / c^2\) is the Schwarzschild radius, the horizon radius.
What aspect of this metric tells you that the geometry is stationary (independent of Schwarzschild time \(t\))?
Schwarzshild's time coordinate \(t\) is special in that it is the unique time coordinate with respect to which the geometry is not only stationary (independent of \(t\)) but also static (all other directions \(x_\alpha\) are orthogonal to the time \(t\) direction, \(g_{t\alpha} = 0\)).
What aspect of this metric tells you that the geometry is spherically symmetric?
What is the proper circumference of a circle at radius \(r\)?
Consider an object “at rest” in the Schwarzschild geometry, satisfying \(dr = d\theta = d\phi = 0\). The “worldline” of such an object is:
A. Timelike;
B. Spacelike;
C. Lightlike;
D. Timelike outside the horizon \(r_s\), lightlike at the horizon, and spacelike inside the horizon;
E. Something else.
Does it make sense to talk about observers at rest at the horizon of a Schwarzschild black hole?
A. Yes.
B. No.
Which of the Schwarzschild coordinates \(t , r , \theta , \phi\), if any, is timelike inside the horizon?
A. \(t\);
B. \(r\);
C. \(\theta\);
D. \(\phi\);
E. None of the above.
Fri 2019 Mar 1:
Will the probe fall into the black hole?
A. Yes.
B. No.
On this unstable circular orbit, if we accelerate forwards, we will:
A. Fall into the black hole;
B. Remain on the unstable circular orbit;
C. Leave the black hole, going far away from it.
Will the probe fall into the black hole?
A. Yes.
B. No.
The tidal force at radius \(r\) outside a spherical mass \(M\) (e.g. a black hole) goes as \(G M / r^3\). What kind of black hole is least likely to tear you apart at its horizon?
A. A stellar-massed black hole (3 to 100 solar masses);
B. A supermassive black hole (\(\geq 10^6\) solar masses);
C. All black holes tear you apart at their horizons.
What will happen at the horizon of the Schwarzschild black hole at the moment you free-fall through it?
A. You will be engulfed in blackness.
B. You will be tidally torn apart.
C. You will encounter an infinitely bright light.
D. Nothing special.
E. Something else.
Wed 2019 Mar 6:
Why is the x-ray sky dominated by objects containing black holes or neutron stars?
From a safe distance, we watch a spherical, pressureless star collapse to a black hole. What will we see?
A. The star will appear to freeze when at the horizon radius, and never collapse.
B. The star will appear to branch into a wormhole and white hole, before becoming a black hole.
C. The star will appear to collapse to a singularity.
When the mass of a black hole increases, its horizon expands. Does the horizon appear to engulf stuff that previously fell through the horizon?
A. Yes, stuff that previously fell into the black hole disappears.
B. No, stuff that previously fell into the black hole remains frozen at the horizon, appearing to expand with the horizon.
If, as seen by an outside observer, a star appears never to collapse through its horizon, does the star ever actually collapse?
A. Yes.
B. No.
Mon 2019 Mar 11:
How should you go about calculating the trajectories of radial lightrays in a spherical geometry such as the Schwarzschild geometry, given its metric?
A. Set \(ds^2 = 0\).
B. Use a complete set of conservation laws associated with symmetries of the geometry (energy, angular momentum, rest mass).
C. Use the geodesic equations.
What lies on the other side of the antihorizon (red line)?
A. Nothing.
B. A white hole and another “parallel” universe.
C. The invisible interior of the star that collapsed to a black hole long ago.
How to get to the Parallel Universe from inside the Black Hole?
A. Accelerate towards the Parallel Universe.
B. Accelerate away from the Parallel Universe.
C. A, then go backwards in time.
D. B, then go backwards in time.
E. Trip.
Fri 2019 Mar 15:
In the BHFS visualization of a black hole, which object is the antihorizon?
A. The gravitationally lensed image of the outside Universe.
B. The Einstein ring.
C. The dark red grid.
D. The blue-white grid.
E. It's not visible in the visualization.
What does the arrowed blue line in the Penrose diagram of the Schwarzschild geometry represent?
A. A possible worldline of a person (timelike line);
B. A possible worldline of light (lightlike line);
C. A possible “now” line, a line of simultaneity (spacelike line).
The horizon lines in the Penrose diagram are:
A. Timelike.
B. Lightlike.
C. Spacelike.
From the point of view of an observer outside the outer horizon of a white hole, is the white hole gravitationally attractive or gravitationally repulsive?
A. Attractive.
B. Repulsive.
C. Neither.
Mon 2019 Apr 1:
What are the units (time, length, mass) of the Hubble constant \(H_0\)? What fundamental property of the Universe does \(H_0\) measure? Why might the measurement of that property not be exact?
Does the Universe have a center?
A. Yes (why?).
B. No (why?).
What is the Universe expanding into?
A. Nothing (then what does expansion mean?).
B. Something (specifically?).
Wed 2019 Apr 3:
What does thermodynamic equilibrium mean? What thing in this room is closest to thermodynamic equilibrium?
A. Your brain.
B. Your body.
C. Chairs and tables.
D. The window.
E. The air.
How can the Cosmic Microwave Background (CMB) be construed as evidence for homogeneity and isotropy given that it provides information only over a 2D surface on the sky?
Does the CMB show a characteristic scale?
A. Yes.
B. No.
Does galaxy clustering show a characteristic scale?
A. Yes.
B. No.
Fri 2019 Apr 5
What is the proper length of this line in terms of the radius \(R\) of the hypersphere, and the angle \(\chi\)?
A. \(R\).
B. \(\chi\).
C. \(R \chi\).
D. \(R \sin\chi\).
E. \(2\pi R\).
Why do astronomers use the cosmic scale factor \(a(t)\) rather than the radius \(R(t)\) of the Universe as a measure of the size of the Universe?
A. The radius \(R\) is defined only for a closed Universe.
B. Relative scales can be measured without knowing an absolute scale.
C. The Einstein equations determine only the evolution of \(a\), not \(R\).
D. Something else.
Wed 2019 Apr 10
What is the diameter of the \(6 \times 10^9\) solar mass M87 supermassive black hole? On what timescale do you expect the black hole to vary?
A. Seconds.
B. Hours.
C. Days.
D. Years.
E. Centuries.
M87 has a redshift of 1200 km/s. What is the distance to M87? Estimate the angular diameter of the M87 black hole as seen from Earth.
Given the angular diameter of M87 and a telescope the diameter of the Earth, what is the longest wavelength at which M87 is barely resolved?
Fri 2019 Apr 12:
Energy conservation in an FLRW universe implies \(n \equiv d \ln \rho / d \ln a = - 3 ( 1 + p / \rho )\). What type of energy-momentum remains constant as the Universe expands?
A. Radiation (\(p / \rho = 1/3\), \(n = -4\)).
B. Matter (\(p / \rho = 0\), \(n = -3\)).
C. Curvature (\(p / \rho = -1/3\), \(n = -2\)).
D. Vacuum (\(p / \rho = -1\), \(n = 0\)).
According to the 2nd Friedmann equation, what type of energy-momentum is at the borderline between attraction and repulsion?
A. Radiation.
B. Matter.
C. Curvature.
D. Vacuum.
Mon 2019 Apr 15:
If wavelengths expand with the Universe, \(\lambda \propto a\), how does the temperature \(T\) of the CMB change with scale factor \(a\)?
A. \(T \propto a\).
B. \(T \propto a^{-1}\).
C. \(T \propto a^{-2}\).
D. \(T \propto a^{-3}\).
E. \(T \propto a^{-4}\).
In cosmology, the redshift \(z\) is related to cosmic scale factor \(a\) by \(1 + z \equiv \lambda_{\rm obs} / \lambda_{\rm emit} = a_0 / a\). The CMB was released at Recombination, when H transition from ionized (opaque) to neutral (transparent) at \(T \approx 3{,}000 ~{\rm K}\). The temperature of the CMB today is \(T \approx 3~{\rm K}\). At approximately what redshift did Recombination occur?
A. \(10^{-3}\).
B. 1.
C. 1000.
D. \(10^{12}\).
E. It depends on cosmological parameters such as \(\Omega_{\rm m}\) and \(\Omega_\Lambda\).
Observations indicate \(\Omega_{\rm m} \approx 0.3\) and \(\Omega_{\rm rad} = \Omega_\gamma + \Omega_\nu \approx 10^{-4}\) (note that \(\Omega_\nu / \Omega_\gamma = \tfrac{7}{8} \times \tfrac{4}{11} \times 3 = 0.95\) for relativistic neutrinos). At approximately what redshift did the Universe change from radiation-dominated to matter-dominated?
A. 3.
B. 30.
C. 300.
D. 3000.
E. It was never radiation-dominated.
Wed 2019 Apr 17:
Normally (that is, except during inflation when the Universe was dominated by vacuum energy), the Hubble parameter \(H\) given by \(H^2 = \frac{8}{3}\pi G \rho\) evolved with cosmic time \(t\) as:
A. \(H \propto t^{-2}\).
B. \(H \propto t^{-1}\).
C. \(H\) was constant.
D. \(H \propto t\).
E. \(H \propto t^2\).
During inflation when the Universe is dominated by vacuum energy, the Hubble parameter \(H\) given by \(H^2 = \frac{8}{3}\pi G \rho\) evolved as:
A. \(H \propto t^{-1}\).
B. \(H\) was constant.
C. \(H \propto a^{-1}\).
The Universe just prior to Recombination is best described as:
A. A Big Bang.
B. Dominated by a dense, gravitationally repulsive, GUT-scale vacuum energy.
C. A dark, transparent void, dominated by non-baryonic cold dark matter.
D. An opaque, ionized, photon-baryon fluid close to thermodynamic equilibrium, with sound speed about \(c / \sqrt{3}\).
E. Stars were forming vigorously, and galaxies were beginning to cluster.
The horizon problem is: How can parts of the CMB more than about 1° apart have almost the same temperature? Why is this a problem?
Mon 2019 Apr 22:
The flatness problem is: How come the Universe is so spatially flat? Why is this a problem?
The expansion problem is: Why is the Universe expanding? Why is this a problem?
Why is the temperature constant during inflation?
At the end of inflation, vacuum energy transforms into particle energy in a burst of entropy creation called “reheating”. But if an FLRW universe conserves entropy (\(dE + p dV = T dS = 0\)), how can the entropy of the Universe increase?
What happened before inflation?
A. There was no before: time itself began (the Hawking-Hartle “no boundary condition” proposal).
B. No one knows, but there must have been a time before inflation (before vacuum domination), because vacuum defines no preferred frame, whereas the Universe has a preferred frame (the frame in which the CMB is at rest).
C. “Eternal inflation”: an even higher density vacuum, the Planck density or more, so high that the vacuum expanded faster than pieces of it could decay, producing a multiverse of Universes.
D. Your proposal here.
Wed 2019 Apr 24:
Why does a rotating black hole bulge out into a spheroid (an ellipse of rotation)?
A. Centrifugal force.
B. Tidal forces.
C. Because rotating black holes have accretion disks.
D. Because rotating black holes emit gravitational waves.
E. In general relativity, the choice of coordinates is arbitrary, and the bulging is just an artifact of the choice of coordinates.
The horizons of a rotating (Kerr) black hole are at \(r_\pm = M \pm \sqrt{M^2 - a^2}\), where \(a\) is the angular momentum per unit mass of the black hole. What is the maximum value of \(a\)? What happens when \(a > M\)?
The inflationary instability at the inner horizon of a rotating black hole causes an exponentially huge growth in the density and interior mass of the black hole. Should the inflationary instability have any effect observable to an outside observer?
A. Yes, the mass and gravity of the black hole should appear to increase.
B. Yes, the inflationary instability would generate gravitational waves which the black hole would radiate away.
C. Yes, the inflationary instability would be able to drive jets emerging from the black hole.
D. Only if the instability creates a baby universe, in which case the baby universe would engulf our Universe.
E. No.
Fri 2019 Apr 26:
A more massive black hole produces Hawking radiation with longer wavelength. Therefore a more massive black hole produces Hawking radiation that is _____ energetic, and therefore has a _____ Hawking temperature.
A. Equally, equal.
B. Less, lower.
C. More, lower.
D. Less, higher.
E. More, higher.
Wien's law is \(\lambda_{\rm peak} T = 3 ~{\rm mm}~{\rm K}\). A 10 solar mass black hole has a Schwarzschild radius of 30 km. Approximately what is the Hawking temperature of a 10 solar mass black hole?
What is the Hawking entropy of the 4 million solar mass black hole at the center of the Milky Way? How does this compare to the entropy in the CMB (the number of photons in the observable Universe)?
Does an infaller continue to see Hawking radiation when they fall through the horizon?
A. Yes, from the (true, event) horizon.
B. Yes, from the illusory horizon (the redshifted, dimming surface of the star that collapsed long ago).
C. B, and also from the sky above.
D. No.
What will Hawking radiation look like (a) at the horizon, (b) near the singularity? Will the temperature (the characteristic frequency of Hawking radiation) be:
A. About zero.
B. Similar to the Hawking temperature seen from outside.
C. Somewhat higher than the Hawking temperature seen from outside.
D. Huge.
Wed 2019 May 1:
Would you vote in favor of making a baby Universe?
2 A. I think that it is immoral to attempt to make a baby Universe. I vote no.
3 B. If this is the only way that our Universe can reproduce, then I think society has a moral duty to make it happen. I vote yes.
3 C. I don't think society should waste resources attempting to make a baby Universe. I vote no.
20 D. I don't have a strong moral opinion, but I support the notion that society should attempt to make a baby Universe. I vote yes.
5 E. I don't really care either way. I probably won't bother to vote.
If society were presented with the one-time opportunity to make a baby Universe, what do you think the eventual outcome would be?
8 A. All out war between the yes and no factions.
5 B. Fierce political discussion, resolved by the democractic process.
15 C. Fierce political discussion, leading to deadlock.
5 D. Nothing. Society would not care, and would just go about its business.
You are the leader of the “No-baby-Universe” faction. You believe deeply that your cause is right. You strive for right. But your faction has lost the vote. What do you do?
2 A. Continue to argue non-violently for your cause.
16 B. Fight for right. Start a guerilla war.
8 C. Spread disinformation about your opponents and their theory of making baby Universes.
6 D. Something else.
How should the movie end?
13 A. As the science says: the people outside the black hole never know whether a baby Universe was made, or what might be the nature of that baby Universe.
3 B. The baby Universe should expand out into the old Universe, destroying it, and starting afresh.
7 C. Somehow there is an unexpected line of communication from inside the black hole to outside, that allows people outside the black hole to discover what happened.
10 D. Postpone the conclusion to a sequel.
0 E. Something else.

Spring 2019 ASTR 3740 Homepage

Updated 2019 May 2