Spring 2021 ASTR 3740 Homepage

Spring 2021 ASTR 3740 General Relativity Midterm Review

This midterm review sheet is posted at http://jila.colorado.edu/~ajsh/courses/astr3740_21/review_mid2.html

The midterm will test the material covered during weeks 6 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 5.

The midterm will be a two-hour, open-book test. You can download the test from canvas, and canvas will time when you downloaded the test. You must upload your answers back to canvas no later than two hours after you downloaded the test; again, canvas will time when you uploaded your answers.

There are 10 questions, of which you should do any 8. Each question is worth 5 points, for a total of 40 points. You get no additional credit for doing more than 8 questions; if you do more, please indicate which 8 questions should be graded.

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:
     

     (Compressive, non-tidal, part of) Curvature = Energy-momentum density

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

4. Metric and curvature.
   • Metric
   • Proper time, distance
   • Geodesics
   • Relation between curvature and tidal forces
   • A gravitational wave is a wave of curvature; what does that mean?

5. 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

6. No Hair Theorem
   • What does it state?
   • When does it apply? When does it not apply?

7. 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

8. Kerr-Newman Geometry.
   • What does it describe?
   • Similarities, differences vs. Reissner-Nordström
   • Oblate spheroidal geometry
   • Ergosphere
   • Ring singularity
   • Antiverse (r < 0)
   • Sisytube
   • What does an infaller experience at the inner horizon?

9. Gravitational Waves.
   • Hulse-Taylor binary pulsar
   • What is LIGO (Laser Interferometer Gravitational-Wave Observatory)? How does it work?
   • GW150914: the first detection of gravitational waves from the merger of two black holes
   • What do waveforms of merging black holes look like? Why?
   • GW170817: fhe first detection of gravitational waves from the merger of two neutron stars

10. Event Horizon Telescope (NOT DONE).
    • What is the EHT (Event Horizon Telescope)? How does it work?
    • What does the image of the M87 black hole look like?
    • How is the mass of the M87 black hole measured from the image?
    • In what way(s) does the image confirm general relativity?

11. Hawking Radiation (NOT DONE).
    • Quantum mechanical origin
    • Black body spectrum
    • Wavelength ≈ horizon size
    • Evaporation
    • Irrelevant to astronomical black holes

Updated 2021 Mar 19