Black Hole silhouetted against the Milky Way Fall 2003 ASTR 2030 Homepage

This final review sheet is posted at

The midterm review sheet is posted at

Fall 2003 ASTR 2030 Final Review

The final will be at 7:30-10:30am (in the MORNING!) of Tue Dec 16, in our usual classroom Hale 270.

The final will test everything cumulatively over the semester, but there will be a greater emphasis on materal covered since the midterm. To remind you, before the midterm we covered the Prologue and Chapters 1 to 3 of Thorne, while after the midterm we covered Chapters 4-9 and 12-14 of Thorne. We also covered the Special Relativity and Falling into a Black Hole websites, the former before the midterm, the latter both before and after the midterm.

To make the grading doable in a reasonable time, the final will be mostly multiple choice, graded by scantron, but there will also be a few short answer questions.

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

The things that I think are most important in what we did before the midterm are:

Review Questions

  1. How to Script a Movie. Describe the 4 parts of a well-structured movie script. For last year's class (Fall 2002) I posted a summary table at

  2. Gravity Power. What happens to a gravitating system when you remove energy from it? In what sense does this mean that gravity is "the perpetual motion machine that drives the Universe"? Give several examples where gravity is the source of energy of an astronomical phenomenon.

  3. 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?

  4. 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.

  5. 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?

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

  7. 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?

  8. 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?

  9. 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?

  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. MAXIM. What does the MAXIM mission plan to do? What kind of telescope will that require?

  17. Tidal Forces. What are tidal forces? Describe tidal forces near a black hole in terms of the river model of black holes. Are tidal forces stronger near more massive or less massive black holes? Explain. How does the presence of tides indicate that spacetime is curved?

  18. Schwarzschild Wormhole. Give an account of the Schwarzschild wormhole. What is it? Do such wormholes exist in real black holes? Why not? If a Schwarzschild wormhole did exist in a real black hole, why could a traveler not pass through the Schwarzschild wormhole? Could the traveler see light from the other side of the wormhole?

  19. White Hole. What is a white hole? Describe it in terms of the river model. Do white holes really exist?

  20. Traversable Wormhole. What is the key ingredient needed for a traversable wormhole, one in which a person could go through the wormhole in both directions (preferably without being killed)? Roughly speaking, why is this ingredient essential? Why don't we just go out and make these wormholes? Explain how one might use a traversable wormhole to violate causality.

  21. Charged Black Holes. 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?

  22. 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?

  23. Rotating Black Holes. 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?

  24. 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?

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

  26. 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?

  27. 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?

Updated 2003 Dec 3