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I'm trying to determine the exact transformation that brings a spherically symmetric spacetime metric in spherical coordinates to the Sylvester normal form (that is, with just 1 or -1 on its main diagonal, with all other elements equal to zero.) Assuming that the metric has Lorentzian signature, does anyone know how to determine the exact transformation that achieves this?

Thanks.

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# Transformation to get a Lorentzian spherically symmetric metric to the Sylvester form

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