Local Conformal Transformations:Coordinate or metric transformations?

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SUMMARY

Local conformal transformations in the context of General Relativity and Shape Dynamics are defined as scalar transformations of the metric rather than coordinate transformations. Specifically, they do not conform to the form \vec{x} \mapsto C(x^{\mu})\vec{x}, where C(x^{\mu}) is a differentiable function. This distinction is crucial for understanding the implications of conformal transformations on spacetime metrics and their physical interpretations.

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Johanna222
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Hello,

I'm wondering what the exact definition of a local conformal transformation is, in the context of General Relativity (/Shape Dynamics)

To be more precise:
1. Are local conformal transformations coordinate transformations or scalar transformations of the metric?
2. If they are coordinate transformations, are they of the form [itex]\vec{x} \mapsto C(x^{\mu})\vec{x}[/itex], with [itex]C(x^{\mu})[/itex] a differentiable function?

Good evening to you all!
 
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