Oct 17
Chapter 7.1
- No one coordinate system is favored over another because there are generally no special symmetries.
- Some coordinates systems have singularities where multiple coordinates are mapped to the same place, for example \(dS^2 = \frac{a^4}{r^{'4}}(dr^{'2} + r^{'2}d\phi^2) \) blows up at \(r^{'} = 0\).
The singularities in most coordinate systems mean that different overlapping coordinate patches must be used
cover space time so that every point is labeled by a nonsingular set of coordinates.
example 7.1
- problem | guess | solution
- a | not obeyed | not obeyed
- b | obeyed | obeyed
- c | obeyed | obeyed
- d | not obeyed | obeyed
- e | not obeyed | not obeyed
- f | obeyed | obeyed
- g | not obeyed | obeyed
- h | not obeyed
- (i) obeyed
- (j) obeyed | not obeyed
- (k) obeyed | not obeyed
- (l) obeyed
8 out of 12 correct
