In Ray d'Inverno's book on general relativity, he defines the volume element in a way which makes it a scalar density of weight -1, meaning it transforms with the inverse of the Jacobian. Every other source I have looked at seems to say it should transform with the Jacobian, making it a scalar density of weight +1. Can anyone clarify this for me?(adsbygoogle = window.adsbygoogle || []).push({});

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# Why is the volume element a scalar density of weight -1?

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