(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the metric ds^{2}=(u^{2}-v^{2})(du^{2}-dv^{2}). I have to find a coordinate system (t,x), such that ds^{2}=dt^{2}-dx^{2}. The same for the metric: ds^{2}=dv^{2}-v^{2}du^{2}.

2. Relevant equations

General coordinate transformation, ds^{2}=g_{ab}dx^{a}dx^{b}

3. The attempt at a solution

I started with a general transformation x^{a}→x'^{a}so the new metric is g'_{μν}=g_{ab}(dx^{a}/dx'^{μ})(dx^{b}/dx'^{ν}). The components of g (old metric) and g'(new metric) are known and the unknowns are the derivatives of the old coordinates with respect to the new ones. That's where I'm stuck.

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# Homework Help: General relativity- Coordinate/metric transformations

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