Spring 2014 ASTR 3740 Homepage

Spring 2014 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 ≡ 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.
   • Formation in core-collapse supernovae
   • X-ray binaries
   • Active Galactic Nuclei (e.g. quasars)
   • Accretion disks
   • Jets
   • Lots of mass in a small space

9. Hawking Radiation.
   • Quantum mechanical origin
   • Black body spectrum
   • Wavelength ≈ horizon size
   • Evaporation
   • Irrelevant to astronomical black holes

10. Curvature.
    • Relation between curvature and tidal forces

    NOT DONE.

11. Gravitational Radiation.

Updated 2014 Mar 12