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I am interested in the discussion in section 10.5 of Schutz's First Course in GR book. Specifically, the conditions at r = 0 of a static, spherically symmetric interior star (or whatever) solution e.g. Schwarzschild interior solution.

He argues that by enforcing local flatness one finds that the radial metric coefficient g_rr is 1 at the origin. Is there some way one can argue as to what the g_tt (g_00 as he writes) would be at the origin? Analysis of specific interiors shows that it is not 1, which makes sense as otherwise there would be no time dilation and thus, to an external observer, no potential. In fact it seems to me quite remarkable that g_rr should be 1 at the origin.

Any tips?

Cheers,

Z

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# Local flatness at r = 0 for star interior spacetime

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