Spring 2007 ASTR 3740 Homepage

Spring 2007 ASTR 3740 General Relativity Midterm Review

The midterm will test the material covered during weeks 6 to 9, which is to say, general relativity and black holes. Obviously, there is a non-trivial overlap with special relativity, so you should not forget what you learned during weeks 1 to 5.

The midterm will be a 50 minute test.

For 2 point questions, your answer should consist of one or two clear, grammatically correct sentences. Answers to questions with more points should be proportionately longer.

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

Review Questions

1. Postulates.
• Existence of local inertial (free-fall) frames
• (Weak/Strong) Principle of Equivalence
• Einstein's equations
 Curvature = Energy-momentum density

2. Consequences of the Equivalence Principle.
• Gravitational redshift
• Gravitational bending of light
• Gravity º curvature of spacetime

3. Mathematics.
• Metric
• Geodesics
• Proper time, distance

4. Schwarzschild Geometry.
• What does it describe?
• What do the various parts of the metric mean?
• Embedding diagram
• Spacetime diagram
• Finkelstein coordinates
• Kruskal coordinates
• Penrose diagram
• River model
• Orbits
• What do things falling in look like from outside?
• What do things look like if you fall in?
• Collapse to a black hole
• Wormhole, white hole, parallel universe, and problems therewith

5. No Hair Theorem

6. Reissner-Nordström Geometry.
• What does it describe?
• Similarities, differences vs. Schwarzschild
• Outer, inner horizons
• Penrose diagram
• River model
• Why are the vacuum solutions inconsistent?
• What does an infaller experience at the inner horizon?
• Mass inflation

7. Kerr-Newman Geometry.
• What does it describe?
• Similarities, differences vs. Reissner-Nordström
• Oblate spheroidal geometry
• Ergosphere
• Ring singularity
• Antiverse (r < 0)
• Closed timelike loops

8. Observational evidence (planetarium show).
• Formation in core-collapse supernovae
• X-ray binaries
• Active Galactic Nuclei (e.g. quasars)
• Accretion disks
• Jets
• Lots of mass in a small space

NOT DONE.