- #1
Master J
- 226
- 0
I have just started self-studying General Relativity with Landau-Lifshitz' Classical theory of Fields, supplementing it with a bit of extra math here and there ( I have an experimental degree).
He introduces curved spacetime by stating that in a non-inertial reference-frame, the space-time interval ds in curved, since it is described by a general quadratic form:
ds[itex]^{2}[/itex] = g[itex]_{ik}[/itex].dx[itex]^{i}[/itex].dx[itex]^{k}[/itex]
That much is obvious to me sinceif one simply takes ds[itex]^{2}[/itex] and graphs it it would sketch a curve. However, it is then stated that the coordinates are curvilinear.
Why is that? Why can't the above equation simply represent a curve, but in orthogonal Cartesian coordinates?
He introduces curved spacetime by stating that in a non-inertial reference-frame, the space-time interval ds in curved, since it is described by a general quadratic form:
ds[itex]^{2}[/itex] = g[itex]_{ik}[/itex].dx[itex]^{i}[/itex].dx[itex]^{k}[/itex]
That much is obvious to me sinceif one simply takes ds[itex]^{2}[/itex] and graphs it it would sketch a curve. However, it is then stated that the coordinates are curvilinear.
Why is that? Why can't the above equation simply represent a curve, but in orthogonal Cartesian coordinates?