| Please study this equation extensively while continuing in multiplying it by itself. | |
| R_μν - 1/2 g_μν R + Λg_μν = κT_μν | |
| (R_μν - 1/2 g_μν R + Λg_μν) * (R_μν - 1/2 g_μν R + Λg_μν) = | |
| R_μν * R_μν - 1/2 g_μν * R_μν * R_μν + Λg_μν * R_μν - 1/2 g_μν * R_μν * g_μν R + Λg_μν * R_μν * g_μν | |
| R_μν * R_μν - 1/2 g_μν * R_μν * R_μν + Λg_μν * R_μν - 1/2 g_μν * R_μν * g_μν R + Λg_μν * R_μν * g_μν = | |
| κT_μν * R_μν - 1/2 κT_μν * g_μν * R_μν + κT_μν * Λg_μν - 1/2 κT_μν * R_μν * g_μν + κT_μν * Λg_μν * g_μν | |
| κT_μν * R_μν - 1/2 (κT_μν * g_μν + κT_μν * Λg_μν) + 1/2 (κT_μν * g_μν * R + κT_μν * Λg_μν * g_μν) = | |
| κT_μν * R_μν - 1/2 κT_μν * g_μν (1 + Λ) + 1/2 κT_μν * g_μν R | |
| κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) + 1/2 κT_μν * g_μν R = | |
| κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) * (1 + 1/2 g_μν) | |
| κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) * (3/2) = | |
| 1.5 * κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) | |
| 1.5 * κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) |