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In flat conformal space-time,

[tex]e.g. \quad g_{\alpha \beta} = e^{4\kappa} \eta_{\alpha \beta}[/tex]

where [tex]\kappa[/tex] is some function of space-time coordinates.

What sort of paths do photons and massive particles follow? Could anyone describe their paths with some analagy or a picture? What is the difference between conformally flat space-time and flat space-time physically?

Moreover, if the space-time is only conformal but not flat, what does this mean physically? Why is conformal /conformal flat space-time useful in GR?

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# Conformal spacetime

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