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It is known that the conformal transformation saves the causal structure of the spacetime. Then, what is the physical interpretation of the singularities of the conformal coefficient?

I know that usually we can transform the metric to conformally flat one and put its singularities in the conformal coefficient such as when we go to the Kruskal coordinate. But, it does not mean that all the singularities of that coefficient is the singularity of the metric.

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  • $\begingroup$ Are you referring to the event horizon? If so it's the Schwarzschild coordinates that are singular not the geometry. $\endgroup$
    – John Rennie
    Sep 3, 2019 at 4:54
  • $\begingroup$ @JohnRennie: No, I mean singularities of a coefficient factor for a general conformal transformation. $\endgroup$
    – Astrolabe
    Sep 3, 2019 at 5:17

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