Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

Just brushing up on my GR for a project and i have a silly question:

For the spherical polar representation of the schwarzschild metric, the fact that there are no infintesimal-cross terms implies that the non-diagonal entries in the matrix representation are zero, correct? I guess what im asking is i know what the matrix looks like in cartesians for minkowski space, but obviously it doesn't look the same in spherical polars. Thus, can i simply take the coefficients of dr^2, dtheta^2 etc from the schwarzschild spacetime interval and plug them in as the diagonal components of g-mu,nu and label the columns/rows as spherical coordinates rather than cartesians?

Hope that made sense :S

Cheers

-G

EDIT: Also, can somebody provide a reference (i had a go at looking but couldn't find anything substantial) to show the metric inside a rigid gravitating body (Shwarz metric only valid r>R of course) or do you have to solve for it directly from the Einstein field equations? Surely this has been done before? Metric inside a static, constant density body?

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# Basic matrix representation question

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