Derive Reissner Nordstrom Eq. (8) Explained

[darida]

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)?

 

[lautaaf]

Contract both sides of (3) with $g^{\mu\nu}$ and you will get a condition for $R$

 

[darida]

Ah thank you, that's so simple >_<

 

[vanhees71]

The trace of the energy-momentum tensor of a classical massless field vanishes because of symmetry under dilations. Now use the hint in #2.