The basic equations are: $$G_{\mu \nu} + \Lambda g_{\mu \nu}= \frac{8\pi G}{c^4} T_{\mu \nu}$$ with $$G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} g_{\mu\nu}R$$ and $$T_{\mu \nu} = g_{\mu \alpha} g_{\nu \beta} T^{\alpha \beta}$$ and $$T^{\alpha \beta} , = \left(\rho + \frac{p}{c^2}\right)u^{\alpha}u^{\beta} + p g^{\alpha \beta}$$