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This Final review sheet is posted at

The Special Relativity midterm review sheet is posted at
and the General Relativity midterm review sheet at

Fall 2006 ASTR 2030 Final Review

The final will be at 4:30-7pm on Monday Dec 18, in our usual classroom Duane G1B020.

The final will test everything cumulatively over the semester, but there will be a greater emphasis on materal covered since the midterm. Check out the weekly summaries, and the clicker questions.

The format will be similar to that of the midterms, only longer. The questions will be mostly multiple choice, graded by scantron (which speeds grading), but there will also be a few short answer questions.

You get -1 point for each time you misspell Schwarzschild.

Review Questions

  1. How to Script a Movie. Describe the 4 parts of a well-structured movie script.

  2. Escape Velocity. During this course we have come across several examples where we have been able to deduce things from the equation v = (2 G M / r)1/2. What do the symbols in this equation signify? Give several examples of where we have applied this equation. In each case, was the equation applied exactly, or just as an order of magnitude estimate?

  3. Cold Matter. Why is a liquid or solid almost "incompressible"? At high enough pressure, a liquid or solid can be compressed; what is the condition for this to occur? What happens then? Give an account of what happens to a sphere of cold matter as you increase its mass. Follow the stages through planet, white dwarf, neutron star, black hole.

  4. White Dwarfs. What is a white dwarf? What kind of pressure supports a white dwarf? Give an account of this pressure. Can particles at zero temperature move? Can matter at zero temperature have a nonzero pressure?

  5. Chandrasekhar Limit. What is the Chandrasekhar Limit? What causes it? What happens if a white dwarf exceeds the Chandrasekhar limit?

  6. Neutron Stars. What is a neutron star? What kind of pressure supports a neutron star? Why are neutrons able to withstand a higher pressure than electrons?

  7. Core Collapse Supernovae. What is a core-collapse supernova? Give an account of the evolution of a massive star just before core collapse. What is the core made of just before core collapse? Why? What has the Chandrasekhar limit got to do with core collapse? How does the core convert into being made of neutrons?

  8. Pulsar. What is a pulsar? The Crab nebula is thought to be the remnant of the Supernova of 1054. How does the Crab nebula support Zwicky's idea that supernovae result from the collapse of the core of a massive star to a neutron star?

  9. Gamma Ray Bursts. What is a gamma ray burst? There are two kinds of gamma ray burst, short and long (roughly, shorter than 2 seconds, and longer than 2 seconds). What is an afterglow? What evidence suggests that long bursts are associated with supernovae? What are gamma ray bursts thought to result from?

  10. X-Ray Binaries. What is an x-ray binary? What produces the x-rays? Why x-rays rather than, say, visible light? How do astronomers conclude that a compact object in an x-ray binary is a neutron star? How do astronomers conclude that a compact object in an x-ray binary is a black hole? Approximately how many x-ray binaries in the Milky Way have measurements indicating that they contain a black hole?

  11. Accretion Disks. What is an accretion disk? What is the observational evidence for accretion disks? Why does material tend to form into an accretion disk rather than falling directly on to a neutron star or black hole? What is the source of energy that heats an accretion disk?

  12. Active Galactic Nuclei. What is an Active Galactic Nucleus (AGN)? Name several phenomena associated with an AGN.

  13. Jets. What is the observational evidence for jets? In what kind of electromagnetic radiation are jets commonly observed? The radiation is mostly synchrotron radiation. What is synchrotron radiation? Two pieces of observations that at at least some jets are moving at very close to the speed of light are (1) superluminal motion, and (2) one-sidedness. Explain what each of these is, and why they are considered to be evidence for relativistic motion.

  14. Supermassive Black Holes. What is a supermassive black hole? Where are they found? What is the evidence that supermassive black holes are indeed black holes? How are the masses of supermassive black holes determined? For approximately how many supermassive black holes have masess been measured?

  15. Sagittario. Give an account of the object at the center of our own Galaxy, the Milky Way. What is SgrA*? How is the mass of Sagittario measured? What is its mass?

  16. Penrose diagrams. What is a Penrose diagram? On a Penrose diagram, draw a possible worldline of (a) a person, (b) a light ray. How are Penrose diagrams useful in explaining black holes?

  17. Charged Black Holes. What does the Reissner-Nordström geometry describe? Given an account of the similarities and differences between the geometries of a spherical black hole with and without electric charge. Describe the charged black hole in terms of the river model. Are real astronomical black holes likely to be charged?

  18. Inner Horizon. What is an inner horizon? Describe it in terms of the river model. What does an infalling person experience at the inner horizon? Why does this mean that the standard vacuum solutions for the interiors of black holes cannot be correct? What actually happens inside the inner horizon?

  19. Reissner-Nordström Wormhole, White Hole. Give an account of the Reissner-Nordström wormhole and white hole.

  20. Rotating Black Holes. What does the Kerr-Newman geometry describe? Sketch a schematic diagram of a rotating black hole. Describe it in terms of the river model. How does the geometry of a rotating black hole differ from that of a charged spherically symmetric black hole? In what ways does the geometry resemble that of a charged spherically symmetric black hole?

  21. The Other Side of the Ring Singularity. In the standard vacuum solution for a rotating black hole, the singularity is a ring, kept open by the centrifugal force. If a person passes through the ring, they go to negative radius, from which vantage point the black hole appears to have negative mass. What weird thing happens in this world at negative radius?

  22. Inside Real Black Holes. How much of all this weird stuff actually happens inside real black holes? What happens in reality?

  23. Hawking Radiation. What is Hawking radiation? Give a rough explanation of how it is produced. What kind of spectrum does it have? The most important thing to know about Hawking radiation is that the characteristic wavelength is roughly equal to the Schwarzschild radius. What does this imply about the Hawking temperature of Hawking radiation? What would a black hole look like if detected in Hawking radiation? Is Hawking radiation from real astronomical black holes observed or observable? Classically, an object that falls into a black hole appears to an outside observer to become extremely redshifted and frozen at the horizon. How does the presence of Hawking radiation modify this picture?

  24. Black Hole Evaporation. Black holes lose mass by Hawking radiation, and can eventually evaporate. For what kind of black hole is evaporation important? Do such black holes exist? Could such black holes exist? Roughly how much energy does an evaporating black hole produce when it explodes?

  25. MAXIM. What does the MAXIM mission plan to do? What kind of telescope will that require? Why must x-ray telescopes observe from space, not from the ground?

  26. Expansion of the Universe. What observation, by whom, led to the notion that the Universe is expanding? What is a Hubble diagram? What is Hubble's Law? Why is Hubble's constant of fundamental interest in cosmology? How does the Hubble constant relate to the age of the Universe? Why?

  27. Geometry of the Universe. What observational evidence suggests that the Universe at large is spatially uniform? If the Universe is spatially uniform, then general relativity restricts the spatial geometry of the Universe to one of just three possibilities - closed, flat, and open. What measurable differences do the three types have? What is W? What does it have to do with the geometry of the Universe?

  28. Dark Energy. What is meant by Dark Energy? In January 1998 two separate teams reported that the Hubble diagram of high redshift Supernovae showed that the Universe was accelerating. What is the connection between this discovery and Dark Energy?

  29. Mass-Energy Content of the Universe. What are the main contributors to the mass-energy content of the Universe?

  30. Horizon. The deeper we look in space, the further back in time we see. Why? What, where, and why is our horizon? What is meant by the edge of the observable Universe? What lies beyond the edge of the observable Universe? Does the Cosmic Background Radiation come from the horizon? What happens to our horizon as time goes by?

  31. Cosmic Microwave Background (CMB). What is the CMB? What kind of spectrum does the CMB have? What is its temperature? Has the CMB always been at the same temperature it is now? Why can we see no further back than the CMB? How does the Microwave Background vary around the sky? Why does the CMB appear slightly hotter in one half of the sky than the other half?

  32. Fluctuations in the CMB. What does the power spectrum of temperature fluctuations in the CMB mean? What can we learn from the power spectrum of fluctuations in the CMB? What is the connection between the horizon size at Recombination, and the position (harmonic number) of the first acoustic peak? How does this provide information about the geometry of the Universe? What have measurements from the Boomerang (2000) balloon, and from the WMAP (2003, 2006) satellite, revealed about the geometry?

  33. Horizon Problem. Explain why regions of the CMB further apart than about 1° were causally disconnected at the time of Recombination. Why does the uniformity of the CMB then pose a problem? This is the Horizon Problem. How does inflation solve the problem? If the Universe is decelerating, does stuff appear or disappear over our horizon? If on the other hand the Universe is accelerating, does stuff appear or disappear over our horizon?

  34. Inflation. What is inflation? What dominates the energy density of the Universe during inflation? What is thought to be the origin of this form of energy? When is inflation thought to have happened? How does the Universe expand during inflation? What happens to the horizon during inflation?

  35. Problems of the Universe. How does inflation solve the following problems:
    1. Why is the Universe expanding?
    2. Why is the Universe at large so smooth, as indicated by the tiny (few × 10-5) fluctuations in the CMB?
    3. Why is the Universe so flat, as indicated by Boomerang and WMAP CMB observations?
    4. The Horizon Problem?
    5. What caused ripples in the smoothness, which later grew by gravity into galaxies, stars, and you?
    6. Where did matter and radiation come from?

 Black Hole silhouetted against the Milky Way Fall 2006 ASTR 2030 Homepage

syllabus | timetable | projects | homework | clicker questions | weekly summaries | books, movies | images

Updated 2006 Dec 11