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).(adsbygoogle = window.adsbygoogle || []).push({});

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 thecoordinatesare curvilinear.

Why is that? Why cant the above equation simply represent a curve, but in orthogonal Cartesian coordinates?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Curved-spacetime, but why curved coordinates?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**