Essays/Schwarzschild/Schwarzschild04
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...
... attempt to obtain the electromagnetic field tensor from the Riemann-Christoffel tensor ...
...
NB. ... script Schwarzschild.ijs (continued) ... eGX00=:(0 0 0 0);(1 0 0 1);(2 0 0 2);(3 0 0 3) eGX01=:(0 0 1 0);(1 0 1 1);(2 0 1 2);(3 0 1 3) eGX02=:(0 0 2 0);(1 0 2 1);(2 0 2 2);(3 0 2 3) eGX03=:(0 0 3 0);(1 0 3 1);(2 0 3 2);(3 0 3 3) eGX10=:(0 1 0 0);(1 1 0 1);(2 1 0 2);(3 1 0 3) eGX11=:(0 1 1 0);(1 1 1 1);(2 1 1 2);(3 1 1 3) eGX12=:(0 1 2 0);(1 1 2 1);(2 1 2 2);(3 1 2 3) eGX13=:(0 1 3 0);(1 1 3 1);(2 1 3 2);(3 1 3 3) eGX20=:(0 2 0 0);(1 2 0 1);(2 2 0 2);(3 2 0 3) eGX21=:(0 2 1 0);(1 2 1 1);(2 2 1 2);(3 2 1 3) eGX22=:(0 2 2 0);(1 2 2 1);(2 2 2 2);(3 2 2 3) eGX23=:(0 2 3 0);(1 2 3 1);(2 2 3 2);(3 2 3 3) eGX30=:(0 3 0 0);(1 3 0 1);(2 3 0 2);(3 3 0 3) eGX31=:(0 3 1 0);(1 3 1 1);(2 3 1 2);(3 3 1 3) eGX32=:(0 3 2 0);(1 3 2 1);(2 3 2 2);(3 3 2 3) eGX33=:(0 3 3 0);(1 3 3 1);(2 3 3 2);(3 3 3 3) eGX0=:eGX00,eGX01,eGX02,:eGX03 eGX1=:eGX10,eGX11,eGX12,:eGX13 eGX2=:eGX20,eGX21,eGX22,:eGX23 eGX3=:eGX30,eGX31,eGX32,:eGX33 eGX4=:eGX0,eGX1,eGX2,:eGX3
NB. ... script Schwarzschild.ijs (continued) ... eGB=:gcn(1 0 2|:])@([smx 1|:])"2 4 B2k
NB. ... script Schwarzschild.ijs (continued) ... eGBX=:+/"1@((<0 3)|:])"4@eGB
NB. ... execute (ijx) ...
eTaC=:1.5,1.5,1.2,1.2,1.5,0"_
eTaP=:100 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_
(10 10$]) (eTaC([(eGBX-:"2 +/"1@(eGX4{])"4@eGB)gs)eTaP)''
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1
NB. ... execute (ijx) ...
eTbC=:1.5,1.5,1.2,1.2,1.5,0"_
eTbP=:100 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_
((2^_44)tsz]) (?.@{.@${]) (eTbC([(eGX4{])"4@eGB gs)eTbP)''
0 0.00163706 0.00163706 _0.00318123
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0.00163706 0 _0.003367 0.00163706
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0.00163706 _0.003367 0.0349033 _0.0332663
0 0 _0.0232689 0.0232689
0 0 0 0
0 0 0 0
0.00722743 _0.00750608 0.0498994 _0.0498994
_0.00318123 0.00163706 _0.0332663 0.0349033
NB. ... script Schwarzschild.ijs (continued) ...
eGAFF3003=:(+/@:|%2:)@((<0 1)|:])@:(+/"1)@(eGX4{])"4@eGB
eGAFF0330=:eGAFF3003
NB. ... script Schwarzschild.ijs (continued) ...
eGAFF0320=:((<3 2){])@:(+/"1)@(eGX4{])"4@eGB
NB. ... script Schwarzschild.ijs (continued) ... eGF=:+/"1@((<1 2)|:])"4@(([gcn gs)*/"2(0.6885303726590539"_)*eGF20)
NB. ... script Schwarzschild.ijs (continued) ...
eGAF03=:((<0 3){])"2@eGF
eGAFp0=:(eGAF03,"0 1[(eGAFF0320,"0 eGAFF3003)gs)
eGAFp1=:(0,0,0,0{]),(0,0,0,0:),(((1{])%0{]),0,0,0:),:((2{])%0{]),0,0,0:
eGAF =:eGAFp1"1@eGAFp0
NB. ... execute (ijx) ... eTcC=:1.5,1.5,1.2,1.2,1.5,0"_ eTcP=:100 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ (10 10$]) (eTcC(eGAF((2^_32)teq[;])"2 eGF)eTcP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Download: File:LSC0400C.txt
Download: File:LSC0401C.txt
Download: File:LSC0402C.txt
Download: File:LSC0403C.txt
Download: File:LSC0404C.txt
Download: File:LSC0405C.txt
Download: File:LSC0406C.txt
Download: File:LSC0407C.txt
Download MoinMoin source: File:Schwarzschild04.ijs
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Contributed by Tom Allen