- #1

MathematicalPhysicist

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## Main Question or Discussion Point

I have the metric ##ds^2=dudv+F(y,z)du^2+dy^2+dz^2##.

I have shown that for ##F(y,z)=0## it's Minkowski metric, but for ##F(y,z)\ne 0 ## I want to calculate Christoffel Symbols, Ricci tensor and scalar, the problem is that the metric ##g_{\mu\nu}## is not diagonal, and I need to find ##g^{\mu\nu}## in order to calculate christoffel and the rest, but how can I solve this without inverting the metric?

Thanks!

I have shown that for ##F(y,z)=0## it's Minkowski metric, but for ##F(y,z)\ne 0 ## I want to calculate Christoffel Symbols, Ricci tensor and scalar, the problem is that the metric ##g_{\mu\nu}## is not diagonal, and I need to find ##g^{\mu\nu}## in order to calculate christoffel and the rest, but how can I solve this without inverting the metric?

Thanks!