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{]


GTEZ2101C.jpg


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


GTEZ2102D.jpg


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


GTEZ2103C.jpg


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


GTEZ2104C.jpg


NB. ... script experimentalZ.ijs ...

udw20=:cos@cw1
udw21=:-@cw0*sin@cw1
udw22=:0:
udw23=:0:

udw2=:udw20,udw21,udw22,udw23


GTEZ2105C.jpg


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


GTEZ2106D.jpg


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


GTEZ2107C.jpg


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


GTEZ2108D.jpg


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


GTEZ2109C.jpg


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


GTEZ2110C.jpg


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'


Zgraphic2100C.jpg
... 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'


Zgraphic2101C.jpg
... 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