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?

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# Curved-spacetime, but why curved coordinates?

Can you offer guidance or do you also need help?

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