3. -


-2 95.5-95.8

\( R_{ik}-\frac{1}{2}g_{ik}R=\frac{8{\pi}G}{c^4}T_{ik} \quad(3.0) \)

\( R_{i}^{k}-\frac{1}{2}{\delta}_{i}^{k}R=\frac{8{\pi}G}{c^4}T_{i}^{k}\quad(3.1) \)

\( R^{ik}-\frac{1}{2}g^{ik}R=\frac{8{\pi}G}{c^4}T^{ik}\quad(3.2) \)

\( R_{ik}=\frac{8{\pi}G}{c^4}(T_{ik}-\frac{1}{2}g_{ik}T)\quad(3.3) \)



\( R_{ik}-\frac{1}{2}g_{ik}R=\frac{8{\pi}G}{c^4}T_{ik}+{\Lambda}g_{ik}\quad(3.4) \)

:

\( R=-\frac{8{\pi}G}{c^4}T \quad(3.5) \)

- . (53.15)

\( R^{km}=(-1/2)g^{il}\frac{\partial^2{g^{km}}}{\partial{x^{i}}\partial{x^{l}}} + g^{jk}g^{qm}g_{np}g^{il}\Gamma^n_{jl}\Gamma^p_{iq} \)

\( g^{il}\Gamma^p_{il}=0 \)