In coordinates given by [itex]x^\mu = (ct,x,y,z)[/itex] the line element is given(adsbygoogle = window.adsbygoogle || []).push({});

[tex](ds)^2 = g_{00} (cdt)^2 + 2g_{oi}(cdt\;dx^i) + g_{ij}dx^idx^j,[/tex]

where the [itex]g_{\mu\nu}[/itex] are the components of the metric tensor and latin indices run from [itex]1-3[/itex]. In the first post-Newtonian approximation the space time metric is completely determined by two potentials [itex] w [/itex] and [itex] w^i [/itex]. The Newtonian potential is contained within [itex] w [/itex] and the relativistic potential is contained with [itex] w^i [/itex]. What I don't understand is:

Often in the literature of the first post newtonian approximation it is just quoted that the components of the metric tensor are given by:

[tex] \begin{split} g_{00} &= -exp(-2w/c^2), \\

g_{0i} &= -4w^i/c^3, \\

g_{ij} &= - \delta_{ij}\left( 1 +2w/c^2 \right). \end{split}[/tex]

How are these metric components derived?

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# A How to obtain components of the metric tensor?

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