Spring 2005 ASTR 2030 Homepage

Spring 2005 ASTR 2030 Review for Fri Feb 25 Midterm

This midterm will test General Relativity and Black Holes. This means Thorne Ch 2 and 3 (supplemented with Ch 6 and 7), and everything we went through in class since Feb 7. You should find the Falling into a Black Hole website useful. Check out the weekly summaries, and the clicker questions.

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

You get -1 point for 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. No hair theorem. What does the "no-hair" theorem of black holes state?

4. 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?

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

6. 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.

7. 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?

8. You approach a Black Hole. 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? See Approaching the Black Hole.

9. You fall into a Black Hole. Give an account of what you experience if you fall into a black hole. Do tides rip you apart before or after you pass the event horizon? Do you see the entire past or future of the Universe pass by? See Falling to the Singularity of the Black Hole. Explain what you experience using the river model of black holes.

10. You watch a friend fall into a Black Hole. Describe what you see. See Orbiting the Black Hole. Explain what you see using the river model of black holes. In particular, explain the redshifting and freezing at the horizon. If nothing can escape from a black hole, how can its gravity escape? How fast does gravity move?

11. 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.

12. 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.

13. Negative mass. Does negative mass exist? Is negative mass gravitationally attractive or repulsive? According the Principle of Equivalence, which way would a small negative mass fall, if you, standing on the surface of the Earth, held it in your hand and dropped it? What have negative mass and wormholes got to do with each other?

14. 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.

Updated 2005 Feb 23.