Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Curved-spacetime, but why curved coordinates?

  1. Nov 7, 2011 #1
    I have just started self-studying General Relativity with Landau-Lifgarbagez' 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 cant the above equation simply represent a curve, but in orthogonal Cartesian coordinates?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?