| Carroll problem | Subject | Estimated difficulty |
|---|---|---|
| Work out Tmn (m,n=0,1,2,3) for the electromagnetic field in d=4 in terms of E and B fields, with a general spacetime metric. Give physical motivations/explanations for each nonzero component of the energy-momentum tensor. What are the Strong, Weak and Null energy conditions for electromagnetic field "matter" , in terms of E and B fields? | Straightforward | |
| 3.15 | Applying Raychaudhuri's equation | Pretty straightforward |
| 3.9 | Weyl tensor and conformal transformations. Note: Please take eqns (3.147), (G.2),(G.8),(G.9) as your starting point. | Moderate |
| 5.5 | Beacon redshift in a black hole background | Moderately difficult |
My office hour exists for explaining GR physics; please feel free to make good use of it. I also encourage students to discuss the general physics behind these questions together, e.g. in a study group. (Your answers must, however, be individual, in accord with principles of academic integrity.)