6 7 2 D O C U M E N T 4 1 8 C A L C U L A T I O N S I N D I A R Y [p. 51] ϕμνuν Eμ ημ = ex ey ez 0 Γστ ρ ρ δΓστ + ∂ξρ ∂xn --------Γστ n ∂ξα ∂xσ -------- -Γατ ρ – ∂ξα ∂xτ -------- -Γσα ρ – ∂2ξρ ∂xσ∂xτ ---------------- -– = Rμν Θμν αgμνΘ += Θμν ϕμαϕνβgαβ = ϕ14 iex –= ϕ31 hx = gαβ δαβ –= Θ 2( e2 h2) – = Θ44 ϕ41 2 . . + + ) –( e2 = = Θ44 αg44Θ + e2 + α(2e2) –= α 1 2 --( - wg. kosm. Probl.) = Rμν Θμν 1 2 --gμνΘ - += R 3Θ = eh---------- mil2 t2 1 V --- ⋅ V dt d ε 1– ( ) 4πc --------------- -[eh] Kraft = V----------- ε 1– 4πc e h ] Impuls V ---------------- ρVv = = v ε 1– 4πρc ------------- e h = ~------------------------------------ 10 2– 10 104 ⋅ ⋅ 3 1010 ⋅ ~3 10 8– ⋅ Rμν 1 2 --gμνR - – Θμν gμνΘ –= 3 4 -–-- 1 4 -–-- Infinitesimal ∂2( xn' ξn)------------------------ – ∂xσ'∂xτ' --------------------------- - ∂( xρ ξρ) + ∂xn - ∂2ξρ ∂xσ∂xτ ---------------- -–= ∂2ϕρ' ∂xσ'∂xτ' ------------------- ∂ ∂xt ------ - ∂ ∂x ' ∂xr ---------ϕrρ ∂xs --------------------------------- dxs dxσ' ∂x ∂xτ' --------t- = ∂2ϕr ∂xs∂xt ---------------. . . = ϕ μν bx by bz ex ey ez hx hy hz dx dy dz ψμν ψμνuσ+.+. λμνσ = hx hy hz 0 1 4 --δμνϕαψαα - ϕμαψνα – 44: 1 2 --(h2 - d2) – 1 2 --( - d2 e2) – + 1 2 --e2( - ε2 1– ) [6] [8] [7]