D O C . 3 1 C A L C U L A T I O N S 6 3 31. Calculations δR [Berlin, after 18 May 1923][1] AD. [30 164]. δR Rμνδgμν = κ 2 -- - gfστfστ κ 2 -- - ggσμgτνfμνfστ κ 2 -- - gαβ gσμgτμfμνfστ He = He δ κ g fμνfστgσμδ gτν κ ggσμgτνfστδfμν + = –gταgνβδgαβ κfσβfσαδgαβ –= +κfμνδfμν Hi κ β - –g –--gμνiμiν κ β - gμνiμiν –-- = = δHi κ β -- - iμiνδgμν – 2-- κ β - iμδiμ – = –gμαgνβδgαβ ∂δfμν ∂xν ------------- +-- κ β - iαiβδgαβ 2-- κ β∂xν - ∂iμ ------- -δfμν + = +-- κ§ β© - ∂iμ ∂xν ------- - ∂iν ∂xβ¹ --------· – δfμν –fμν 1§ β© -- - ∂iμ ∂xν ------- - ∂xμ¹ --------·νi∂ – = ∂fμν ---------- iμ = ∂fμν ∂xν –---------- iμ 1 β -- - iμ = = [2] [3]