Black Hole silhouetted against the Milky Way Fall 2009 ASTR 2030 Homepage

Fall 2009 ASTR 2030 Review for Th Oct 22 Midterm

This midterm will test General Relativity and Black Holes, which means everything we went through in class from Sep 22 onwards. The midterm will not test Special Relativity, except insofar as it impacts General Relavity. Useful resources:

What parts of Thorne's book will the midterm cover? Of course, I hope that by this time you have read the entire book cover to cover. It's a fabulous book that narrates a vast amount of history that I have only been able to touch on here and there in the lectures. But you want to know what the midterm will test. First, definitely Chs 2 and 3. The test will not cover Chs 4 or 5, which will be addressed later in the semester. The test will cover Ch 6, but only the second half, from page 244 on, where you can read about how the misunderstanding over the nature of black holes finally got resolved. The test will cover Chs 8 and 9, which tell the stories of the discovery of stellar-mass black holes, and then of supermassive black holes. Finally, the lectures have covered some of the issues about what happens inside black holes, which Thorne addresses in Chs 13 and 14. However, there is not much intersection between what the lectures covered and what Thorne discusses, so the test will not cover Chs 13 or 14.

The midterm will be a 50 minute test. It will consist of 20 multiple choice questions, each worth 1 point, plus two short answer questions, each worth 5 points. and 2 short answer questions worth 5 points each, for a maximum possible 30 points.

You get −1 point each time you misspell Schwarzschild.

Review Questions

  1. Redshift, blueshift. What is a redshift or blueshift? How is the rate at which an emitter's clock ticks (as seen through a telescope) related to its observed redshift? How is the brightness (number of photons observed per unit time) of the emitter related to its observed redshift?

  2. Timelike, lightlike, spacelike. In special and general relativity, an interval of spacetime (a short line segment between two events) can be categorized as timelike, lightlike, or spacelike. What do these terms mean?

  3. Postulates of General Relativity. What are the postulates of General Relativity? What is a locally inertial frame? What is a free-fall frame? Qualitatively, what do Einstein's equations relate?

  4. Principle of Equivalence. What is the Principle of Equivalence? From the Principle of Equivalence deduce: (a) the existence of gravitational redshift; (b) that gravity must bend the path of light; (c) that spacetime is curved.

  5. Tidal force. The tidal force is the difference in the gravitational force between the different parts of an object. The presence of tidal forces is the physical manifestation of the curvature of spacetime. Can spacetime be curved in an empty region of space?

  6. 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?

  7. 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?

  8. 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?

  9. Gamma Ray Bursts. What is a gamma ray burst? There are two kinds of gamma ray burst, short and long duration (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 evidence suggests that short bursts are associated with the merger of two neutron stars or of a neutron star and a black hole? What are gamma ray bursts thought to result from?

  10. No-hair theorem. What does the “no-hair” theorem of black holes state?

  11. River model of black holes. Explain to a friend the river model of black holes. At what speed does the river fall? What happens when the river exceeds the speed of light? If nothing can move faster than light, how can the river move faster than light? See A Black Hole is a Waterfall of Space.

  12. Schwarzschild black hole. A Schwarzschild black hole is the simplest kind of black hole, a black hole with mass, but no electric charge, and no spin. Give an account of what you see watching a friend fall into a Schwarzschild black hole. Explain the redshifting and freezing at the horizon in terms of the river model of black holes. Give an account of what you see if you fall into a Schwarzschild black hole yourself. Use the river model to explain how this account can be reconciled with the view of an outside observer watching you fall in. Explain how you can see multiple images of the same object when you approach a black hole. What is the difference between a stable and an unstable orbit? What is the photon sphere? Do tides rip you apart before or after you pass the horizon? What happens at the horizon? What happens when you approach and then meet the central singularity? See Falling into a Black Hole: approach; orbit; singularity; or alternatively, Journey into a Schwarzschild black hole.

  13. Schwarzschild geometry. How do you spell Schwarzschild? What does the Schwarzschild geometry represent? What is the Schwarzschild radius? What is an embedding diagram? Fill in an embedding diagram of the Schwarzschild geometry. See More about the Schwarzschild Geometry.

  14. Schwarzschild wormhole, white hole. Give an account of the complete mathematical Schwarzschild geometry, which consists of a white hole, a black hole, and two universes connected by a wormhole. Explain how the Schwarzschild wormhole is not traversable. See White Holes and Wormholes.

  15. Collapse to a black hole. When a star collapses to a black hole, it appears to freeze forever at the horizon. Does the star really collapse? What does Thorne say about what Einstein and other scientists up to the 1950s thought about this issue? Does collapse to a black hole lead to a wormhole or white hole? See Collapse of a Black Hole.

  16. Penrose diagram. 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 understanding black holes? See Penrose diagrams.

  17. Reissner-Nordström (charged) black hole. 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 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. See Journey into a Reissner-Nordström (charged) black hole.

  20. Kerr (rotating) black hole. 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? 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 (in ellipsoidal coordinates), from which vantage point the black hole appears to have negative mass. What weird thing happens in this world at negative radius? See The Kerr waterfall.

  21. Inside a real black hole. How much of all this weird stuff actually happens inside a real astronomical black hole?

Updated 2009 Oct 17