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

In special relativity the metric is invariant under lorentz transformations and therefore so is the determinant of the metric. How does the metric determinant transform under a more general transformation $$x^{a\prime}=J^{a\prime}_{\quad a}x^{a}$$ where $$J^{a\prime}_{\quad a}$$ may not satisfy the conditions of the lorentz group.

2. Relevant equations

$$x^{a\prime}=J^{a\prime}_{\quad a}x^{a}$$

3. The attempt at a solution

So I need to show how the determinant transforms, but in general I thought that the determinant was a scalar and thus did not transform, clearly this isn't correct so my next thought was to perform the above transformation on the metric as follows:

$$\eta_{a^{\prime}b^{\prime}}=J_{a\prime}^{\quad a}J_{b\prime}^{\quad b}\eta_{ab}$$

Then take the determinant of the result. But this doesn't appear to get me anywhere and doesn't make use of the fact that J is in general not a lorentz transform, any guidance as to where I should go next or whether i'm barking up the wrong tree entirely would be much appreciated :)

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# Homework Help: How does the determinant of the metric transform

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