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


GSC0400C.jpg


NB. ... script Schwarzschild.ijs (continued) ...

eGB=:gcn(1 0 2|:])@([smx 1|:])"2 4 B2k


GSC0401C.jpg


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


GSC0402C.jpg


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


GSC0403C.jpg


NB. ... script Schwarzschild.ijs (continued) ...

eGAFF3003=:(+/@:|%2:)@((<0 1)|:])@:(+/"1)@(eGX4{])"4@eGB
eGAFF0330=:eGAFF3003


GSC0404C.jpg


NB. ... script Schwarzschild.ijs (continued) ...

eGAFF0320=:((<3 2){])@:(+/"1)@(eGX4{])"4@eGB


GSC0405C.jpg


NB. ... script Schwarzschild.ijs (continued) ...

eGF=:+/"1@((<1 2)|:])"4@(([gcn gs)*/"2(0.6885303726590539"_)*eGF20)


GSC0406C.jpg


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


GSC0407C.jpg


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