Spring 2019 ASTR 3740 Homepage

Spring 2019 ASTR 3740 General Relativity Midterm Review

This midterm review sheet is posted at http://jila.colorado.edu/~ajsh/courses/astr3740_19/review_mid2.html

The midterm will test the material covered during weeks 5 to 10 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 4.

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

2. Postulates.
   • Existence of local inertial (free-fall) frames
   • (Weak/Strong) Principle of Equivalence
   • Einstein's equations
     

     Curvature = Energy-momentum density

3. Consequences of the Equivalence Principle.
   • Gravitational redshift
   • Gravitational bending of light
   • Gravity ≡ curvature of spacetime

4. Curvature.
   • Relation between curvature and tidal forces

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

6. 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

7. No Hair Theorem

8. 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

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

10. Hawking Radiation (DONE AFTER SPRING BREAK).
    • Quantum mechanical origin
    • Black body spectrum
    • Wavelength ≈ horizon size
    • Evaporation
    • Irrelevant to astronomical black holes

Updated 2019 Apr 29