Local Conformal Transformations:Coordinate or metric transformations?

AI Thread Summary
Local conformal transformations in General Relativity, particularly in the context of Shape Dynamics, are discussed regarding their nature as either coordinate transformations or metric transformations. The inquiry specifically questions whether these transformations can be defined as coordinate transformations of the form \vec{x} \mapsto C(x^{\mu})\vec{x}, where C(x^{\mu}) is a differentiable function. The discussion highlights the need for clarity on the definition and implications of local conformal transformations in theoretical frameworks. Additional information or insights from participants may further enhance understanding. The conversation emphasizes the importance of precise definitions in the study of conformal transformations.
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 \vec{x} \mapsto C(x^{\mu})\vec{x}, with C(x^{\mu}) a differentiable function?

Good evening to you all!
 
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