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micomaco86572
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I was reading some papers about Lemaitre-Tolman-Bondi model these days, and was confused about the dimension of this metric.
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}$[/tex].
In my GR lessons I was told that the metric is dimensionless. But here something seems to be paradoxical. If the coefficient of the second term is dimensionless, then we can deduce that R must has a dimension of length, which would conflict with the fact that the coefficient fo the thrid term, R, is required to be dimensionless. And vice versa.Forgive my poor English. lol.
As we know, the parabolic LTB line element takes the form:[tex]$ 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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