Essays/Schwarzschild/Schwarzschild05

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GSC0500C.jpg


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

hscv      =:gcv      +gXU*R20i
hscvdx    =:gcvdx    +gXU*R20idx
hscvdxdx  =:gcvdxdx  +gXU*R20idxdx
hscvdxdxdx=:gcvdxdxdx+gXU*R20idxdxdx


NB. ... execute (ijx) ...

   fTaC=:1.5,1.5,1.2,1.2,1.5,1"_
   fTaP=:16 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_

   fTa0=:[hscvdx gs
   fTa1=:(0|:[:(fTaC([hscv gs)])D.1])"1
   (4 4$]) (fTaC(fTa0(((2^_39);2^_20)tcm[;])"3 fTa1)fTaP)''
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1

   fTa2=:[hscvdxdx gs
   fTa3=:(0|:[:(fTaC([hscvdx gs)])D.1])"1
   (4 4$]) (fTaC(fTa2(((2^_33);2^_18)tcm[;])"4 fTa3)fTaP)''
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1

   fTa4=:[hscvdxdxdx gs
   fTa5=:(0|:[:(fTaC([hscvdxdx gs)])D.1])"1
   (4 4$]) (fTaC(fTa4(((2^_28);2^_11)tcm[;])"5 fTa5)fTaP)''
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1


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

hs=:[(hscv;hscvdx;hscvdxdx;hscvdxdxdx)gs


NB. ... execute (ijx) ...

   fTbC=:1.5,1.5,1.2,1.2,1.5,1"_
   fTbP=:16 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_

NB. ... Bianchi identity ...

   (4 4$]) *./^:6"5 (0=]) ((2^_39)tsz]) (fTbC([Bianchi hs)fTbP)''
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1

NB. ... divergence of Einstein's tensor is zero ...

   (4 4$]) *./"1 (0=]) ((2^_44)tsz]) (fTbC([Ediv hs)fTbP)''
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1


GSC0501C.jpg


NB. ... plot (ijs) ...

load 'plot'

gg=:gs                                NB. ... set the metric ...

vS00type  =:1"_                       NB. ... (blue/red) ...
vS01config=:1.5,1.5,1.2,1.2,0,0"_
vS03xH    =:5.7,0.5p1,0,0"_
vS05dxH   =:0,0,0.01,0.07"_
vS06ctrl  =:1,_,_,_,_,_"_
vS11count =:0,600"_
pd vSgDplot vSgD@vS''

vS00type  =:1"_
vS01config=:1.5,1.5,1.2,1.2,0,0"_
vS03xH    =:5.7,0.5p1,0,0"_
vS05dxH   =:0,0,_0.01,0.07"_
vS06ctrl  =:1,_,_,_,_,_"_
vS11count =:0,600"_
pd vSgDplot vSgD@vS''


gg=:hs                                NB. ... set the metric ...

vS00type  =:1"_                       NB. ... outer ...
vS01config=:1.5,1.5,1.2,1.2,0,50"_
vS03xH    =:5.7,0.5p1,0,0"_
vS05dxH   =:0,0,0.01,0.07"_
vS06ctrl  =:1,_,_,_,_,_"_
vS11count =:0,600"_
pd vSgDplot vSgD@vS''

vS00type  =:1"_
vS01config=:1.5,1.5,1.2,1.2,0,50"_
vS03xH    =:5.7,0.5p1,0,0"_
vS05dxH   =:0,0,_0.01,0.07"_
vS06ctrl  =:1,_,_,_,_,_"_
vS11count =:0,600"_
pd vSgDplot vSgD@vS''

vS00type  =:1"_
vS01config=:1.5,1.5,1.2,1.2,0,10"_
vS03xH    =:5.7,0.5p1,0,0"_
vS05dxH   =:0,0,0.01,0.07"_
vS06ctrl  =:1,_,_,_,_,_"_
vS11count =:0,600"_
pd vSgDplot vSgD@vS''

vS00type  =:1"_
vS01config=:1.5,1.5,1.2,1.2,0,10"_
vS03xH    =:5.7,0.5p1,0,0"_
vS05dxH   =:0,0,_0.01,0.07"_
vS06ctrl  =:1,_,_,_,_,_"_
vS11count =:0,600"_
pd vSgDplot vSgD@vS''

vS00type  =:1"_                        NB. ... inner ...
vS01config=:1.5,1.5,1.2,1.2,0,_10"_
vS03xH    =:5.7,0.5p1,0,0"_
vS05dxH   =:0,0,0.01,0.07"_
vS06ctrl  =:1,_,_,_,_,_"_
vS11count =:0,600"_
pd vSgDplot vSgD@vS''

vS00type  =:1"_
vS01config=:1.5,1.5,1.2,1.2,0,_10"_
vS03xH    =:5.7,0.5p1,0,0"_
vS05dxH   =:0,0,_0.01,0.07"_
vS06ctrl  =:1,_,_,_,_,_"_
vS11count =:0,600"_
pd vSgDplot vSgD@vS''

pd 'pdf'
pd 'show'


SCSchwarzschild0500.jpg



Download: File:LSC0500C.txt
Download: File:LSC0501C.txt




Download MoinMoin source: File:Schwarzschild05.ijs




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Contributed by Tom Allen