I was reading some papers about Lemaitre-Tolman-Bondi model these days, and was confused about the dimension of this metric.(adsbygoogle = window.adsbygoogle || []).push({});

As we know, the parabolic LTB line element takes the form:[tex]$ ds^{2}=-c^{2}dt^{2}+(R')^{2}dr^{2}+R^{2}d\Omega^{2}$[/tex].

In my GR lessons I was told that the metric is dimensionless. But here something seems to be paradoxical. If the coefficient of the second term is dimensionless, then we can deduce that R must has a dimension of length, which would conflict with the fact that the coefficient fo the thrid term, R, is required to be dimensionless. And vice versa.

Forgive my poor English. lol.

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# About LTB metric

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