astro 421 homework assignments

Astrophysics 421 Homework Assignments

You are expected to turn in the following homework assignments during the semester, by the dates listed. The assignment list and due dates will be filled out chapter by chapter as we go through the material, so you need to check this page regularly for new assignments and their due dates. The homework assignments correspond to the numbered problems at the end of each chapter in Modern General Relativity: Black Holes, Gravitational Waves, and Cosmology, Mike Guidry (Cambridge University Press, 2019). These will not be graded but will be be checked for completion. This counts 30% of your grade. You may be penalized 25% per day for each day that an assignment is late. This is meant to keep you from getting behind; if there are reasons why you need to be late with an assignment, check with me and we can probably reach an arrangement if your reason is legitimate.

Where solutions are provided, you are expected to do the homework before consulting the solutions. You may work together on the homework assignments as long as each person is doing all the problems (That is, it is not permissible for a team to divide up the work and then copy from each other). You are encouraged to use tools like Maple, Mathematica, MatLab, or programming languages in solving problems and graphing solutions. However, you may not use “black-box” programs written by others to do problems automatically. For example, there are tensor algebra packages in Maple or Mathematica that will solve some general relativity problems automatically. You should learn to use those, but unless I tell you otherwise, I expect you to solve those homework problems by hand, because you also need to learn how the problems are solved. But you can check the answers with the tensor algebra packages and they are valuable tools that you should learn to use in practical applications, once you understand how the tensor algebra works.

Chapter	Assigned Exercises⁺	Due Date*
1. Introduction	None	---
2. Coordinate Systems and Transformations	3, 5, 6	*
3. Tensors and Covariance	1, 7, 22	*
4. Lorentz Covariance and Special Relativity	2, 3, 13	*
5. Lorentz-Invariant Dynamics	7, 10	*
6. The Principle of Equivalence	4, 5, 7	*
7. Curved Spacetime and General Covariance	3, 5, 17	*
8. The General Theory of Relativity	1, 3, 4	*
9. The Schwarzschild Spacetime	3, 12	*
10. Neutron Stars and Pulsars	2	*
11. Spherical Black Holes	3, 12, 15	*
12. Quantum Black Holes	1	*
13. Rotating Black Holes	2, 6	*
14. Observational Evidence for Black Holes	1	*
15. Black Holes as Central Engines	2	*
16. The Hubble Expansion	4, 6	*
17. Energy and Matter in the Universe	1, 6	*
18. Friedmann Cosmologies	1, 6	*
19. Evolution of the Universe	2, 5	*
20. The Big Bang	1, 2	*
21. Extending Classical Big Bang Theory	5	*
22. Gravitational Waves	7	*
23. Weak Sources of Gravitational Waves	1	*
24. Strong Sources of Gravitational Waves	1	*
25. Tests of General Relativity	None	*
26. Beyond Standard Models	None	*

*Unless otherwise noted, homework is due 1 week after finishing corresponding chapter.
⁺If any problems are within parentheses ( ), they are optional extra credit.