Derive Reissner Nordstrom Eq. (8) Explained

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I want to derive Reissner Nordstrom solution using this paper as a guide: http://gmammado.mysite.syr.edu/notes/RN_Metric.pdf, but I get confused by the Eq. (8). Why the Enstein's equation can be rewritten in that form and what is the physical meaning of the Eq. (8)?
 
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Contract both sides of (3) with ##g^{\mu\nu}## and you will get a condition for ##R##
 
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Ah thank you, that's so simple >_<
 
The trace of the energy-momentum tensor of a classical massless field vanishes because of symmetry under dilations. Now use the hint in #2.
 
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