- #1

grelade

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Hi, i was thinking about the metric tensor transformation law:

[tex]g_{cd}(x) = \frac{{dx'}^a}{{dx}^c} \frac{{dx'}^b}{{dx}^d} g'_{ab}(x')[/tex]

and, in view of this definition, the differences between Poincare transformations and reparametrization-like transformation (f.e. various conformal transformations of Schwarzschild metric to obtain Penrose diagrams). Maybe someone could point out the differences between them? I think there should be some because Poincare represent some physical situation whereas reparametrization is just change of coordinate charts. I've read about Poincare transformations being an isometry which suppose to mean that they preserve the manifold structure but I am not sure about this. Hope someone will clarify this.

Thanks for reply in advance.

[tex]g_{cd}(x) = \frac{{dx'}^a}{{dx}^c} \frac{{dx'}^b}{{dx}^d} g'_{ab}(x')[/tex]

and, in view of this definition, the differences between Poincare transformations and reparametrization-like transformation (f.e. various conformal transformations of Schwarzschild metric to obtain Penrose diagrams). Maybe someone could point out the differences between them? I think there should be some because Poincare represent some physical situation whereas reparametrization is just change of coordinate charts. I've read about Poincare transformations being an isometry which suppose to mean that they preserve the manifold structure but I am not sure about this. Hope someone will clarify this.

Thanks for reply in advance.

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