User:Tom Allen/TensorExperimentsZ21
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...
... given spherical symmetry ...
... for convenient presentation ...
... transform space coordinates ...
...
NB. ... script experimentalZ.ijs ...
cw0=:0{]
cw1=:1{]
cw2=:2{]
cw3=:3{]
NB. ... script experimentalZ.ijs ... u0=:cw0*sin@cw1*cos@cw2 u1=:cw0*sin@cw1*sin@cw2 u2=:cw0*cos@cw1 u3=:cw3 uc=:u0,u1,u2,u3
NB. ... script experimentalZ.ijs ... udw00=:sin@cw1*cos@cw2 udw01=:cw0*cos@cw1*cos@cw2 udw02=:-@cw0*sin@cw1*sin@cw2 udw03=:0: udw0=:udw00,udw01,udw02,udw03
NB. ... script experimentalZ.ijs ... udw10=:sin@cw1*sin@cw2 udw11=:cw0*cos@cw1*sin@cw2 udw12=:cw0*sin@cw1*cos@cw2 udw13=:0: udw1=:udw10,udw11,udw12,udw13
NB. ... script experimentalZ.ijs ... udw20=:cos@cw1 udw21=:-@cw0*sin@cw1 udw22=:0: udw23=:0: udw2=:udw20,udw21,udw22,udw23
NB. ... script experimentalZ.ijs ... udw30=:0: udw31=:0: udw32=:0: udw33=:1: udw3=:udw30,udw31,udw32,udw33
NB. ... script experimentalZ.ijs ... udw=:udw0,udw1,udw2,:udw3
NB. ... execute (ijx) ... gXcw =: 0 0 _ _ _"_ gXpAll=: 0 0 0 0 0"_ xwCpts=:_ 1 3 26,_ 0 1p1 26,_ 0 2p1 26,:_ 0 20 26"_ (gXT(([ydx hkxAB)-:"2 udw"_ 1)]) ((0.1;50"_)pTRandom xwCpts)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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. ... script experimentalZ.ijs ... w0=:((cu0^2:)+(cu1^2:)+cu2^2:)^0.5"_ w1=:arctan@(cu2,((cu0^2:)+cu1^2:)^0.5"_) w2=:arctan@(cu0,cu1) w3=:cu3 wc=:w0,w1,w2,w3
NB. ... script experimentalZ.ijs ... swdu0=:0.5*((cu0^2:)+(cu1^2:)+cu2^2:)^_0.5"_ wdu00=:swdu0*2*cu0 wdu01=:swdu0*2*cu1 wdu02=:swdu0*2*cu2 wdu03=:0: wdu0=:wdu00,wdu01,wdu02,wdu03
NB. ... script experimentalZ.ijs ... swdu10=:(cu0^2:)+(cu1^2:)+cu2^2: swdu11=:(cu0^2:)+cu1^2: wdu10=:cu2*(swdu10^_1:)*cu0*swdu11^_0.5"_ wdu11=:cu2*(swdu10^_1:)*cu1*swdu11^_0.5"_ wdu12=:-@(swdu10^_1:)*swdu11^0.5"_ wdu13=:0: wdu1=:wdu10,wdu11,wdu12,wdu13
NB. ... script experimentalZ.ijs ... swdu20=:(cu0^2:)+cu1^2: wdu20=:-@cu1*swdu20^_1: wdu21=:cu0*swdu20^_1: wdu22=:0: wdu23=:0: wdu2=:wdu20,wdu21,wdu22,wdu23
NB. ... script experimentalZ.ijs ... wdu30=:0: wdu31=:0: wdu32=:0: wdu33=:1: wdu3=:wdu30,wdu31,wdu32,wdu33
NB. ... script experimentalZ.ijs ... wdu=:wdu0,wdu1,wdu2,:wdu3
NB. ... execute (ijx) ... gXcw =: 0 0 _ _ _"_ gXpAll=: 0 0 0 0 0"_ yuCpts=:_ 0.000001 5 8,_ 0.000001 5 8,_ 0.000001 5 8,:_ 0 20 8"_ (gXT(([xdy hkyAB)-:"2 wdu"_ 1)]) ((0;50"_)pTRandom yuCpts)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
...
... in Cartesian coordinates on the plane with y2=0 ...
... calculation of components of the divergence of spacetime ...
...
load 'plot'
gXcw =. 1 0 _ _ _ "_
gXpAll=. 1 1 1 2 _0.6"_
yCpts=._ 1p1 3p1 1000,_ 0 0 0,_ 0 0 0,:_ 0 0 0"_
pd (gXT(cy0"_ 1;[(0{])"1@E1cn yRef@hkyG)]) pTtotal yCpts'' NB. ... blue ...
pd (gXT(cy0"_ 1;[(1{])"1@E1cn yRef@hkyG)]) pTtotal yCpts'' NB. ... red ...
pd (gXT(cy0"_ 1;[(2{])"1@E1cn yRef@hkyG)]) pTtotal yCpts'' NB. ... green ...
pd (gXT(cy0"_ 1;[(3{])"1@E1cn yRef@hkyG)]) pTtotal yCpts'' NB. ... purple ...
pd 'pdf'
pd 'show'
... calculated in Cartesian coordinates ...
...
... and ...
... equivalent components calculated in spherical coordinates ...
...
load 'plot'
gXcw =. 1 0 _ _ _ "_
gXpAll=. 1 1 1 2 _0.6"_
xCpts=._ 1p1 3p1 1000,_ 0.5p1 0.5p1 0,_ 0 0 0,:_ 0 0 0"_
pd (gXT(cx0"_ 1;[(0{])"1@E1cn xRef@hkxF)]) pTtotal xCpts'' NB. ... blue ...
pd (gXT(cx0"_ 1;[(1{])"1@E1cn xRef@hkxF)]) pTtotal xCpts'' NB. ... red ...
pd (gXT(cx0"_ 1;[(2{])"1@E1cn xRef@hkxF)]) pTtotal xCpts'' NB. ... green ...
pd (gXT(cx0"_ 1;[(3{])"1@E1cn xRef@hkxF)]) pTtotal xCpts'' NB. ... purple ...
pd 'pdf'
pd 'show'
... calculated in spherical coordinates ...
Download: File:LTEZ2101C.txt
Download: File:LTEZ2102D.txt
Download: File:LTEZ2103C.txt
Download: File:LTEZ2104C.txt
Download: File:LTEZ2105C.txt
Download: File:LTEZ2106D.txt
Download: File:LTEZ2107C.txt
Download: File:LTEZ2108D.txt
Download: File:LTEZ2109C.txt
Download: File:LTEZ2110C.txt
Download MoinMoin source: File:TensorExperimentsZ21.ijs