Umbra

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@John Fredsted Works like a champ! ...

Answered: Umbra 5

April 08 2017

0 0

@John Fredsted Works like a champ! Thank you sir, I'm extremely grateful.

@John Fredsted Physics package ...

Answered: Umbra 5

April 08 2017

0 0

@John Fredsted Physics package is really helpful for a four-dimensional metric. But I'd like to work on a five-dimensional metric. I tried to setup a 5D coordinate system.

But it didn't work.

"Error, (in Physics:-Setup) expected a list with 4 names, where 4 is the spacetime dimension, or one of the keywords cartesian, spherical, cylindrical; received: [t, r, theta, phi, y]"

So I'm using the GRTensor II package.

@gkokovidis Thank you Georgios for ...

Answered: Umbra 5

April 07 2017

0 4

@gkokovidis Thank you Georgios for your reply. I'm using GRTensor II package to calculate the scalar quantity R^{MNQL}R_{MNQL}. I'm attaching the worksheet if it might help. simplify(%) just gives me the same quantity.Shwarzchild_mteric.mw

>	$libname := libname, "d:\\MapleStuff\\grtensor\\lib";$

$"D:\Program Files\Maple 18\lib", ".", "d:\MapleStuff\grtensor\lib"$

[Asym, KillingCoords, PetrovReport, Sym, autoAlias, difftool, grDalias, gralter, grapply, grarray, grcalc, grcalc1, grcalcalter, grcalcd, grclear, grcomponent, grconstraint, grdata, grdebug, grdef, grdisplay, grdump, greqn2set, grinit, grload, grmap, grmetric, grnewmetric, grnormalize, groptions, grsaveg, grtestinput, grtransform, grundef, hypersurf, join, kdelta, makeg, nprotate, nptetrad, qload]

$"d:\MapleStuff\grtensor\metrics"$

(1)

Calculated ds for Scwarzchild (0.000000 sec.)

` ds`^2 = (-1+2*G*M/r)*` d`*t^`2 `+` d`*r^`2 `/(1-2*G*M/r)+r^2*` d`*theta^`2 `+r^2*sin(theta)^2*` d`*phi^`2 `

(2)

Created definition for R(up,up,up,up)

Calculated g(dn,dn,pdn) for Scwarzchild (0.000000 sec.)
Calculated Chr(dn,dn,dn) for Scwarzchild (0.000000 sec.)
Calculated detg for Scwarzchild (0.000000 sec.)
Calculated g(up,up) for Scwarzchild (0.016000 sec.)
Calculated R(dn,dn,dn,dn) for Scwarzchild (0.016000 sec.)
Calculated R(up,up,dn,dn) for Scwarzchild (0.000000 sec.)
Calculated R(up,up,up,up) for Scwarzchild (0.078000 sec.)
Calculated Chr(dn,dn,up) for Scwarzchild (0.015000 sec.)
Calculated R(dn,dn) for Scwarzchild (0.000000 sec.)
Calculated Ricciscalar for Scwarzchild (0.000000 sec.)

(3)

`R `[t]*``[phi]*` `[t]*` `[phi] = -(2*G*M-r)*G*M*sin(theta)^2/r^2

`R `[r]*``[phi]*` `[r]*` `[phi] = G*M*sin(theta)^2/(2*G*M-r)

`R `^phi*``^t*` `^phi*` `^t = -G*M/(r^4*sin(theta)^2*(2*G*M-r))

`R `^t*``^phi*` `^phi*` `^t = G*M/(r^4*sin(theta)^2*(2*G*M-r))

`R `^phi*``^r*` `^phi*` `^r = (2*G*M-r)*G*M/(r^6*sin(theta)^2)

`R `^r*``^phi*` `^phi*` `^r = -(2*G*M-r)*G*M/(r^6*sin(theta)^2)

`R `^phi*``^theta*` `^phi*` `^theta = 2*G*M/(r^7*sin(theta)^2)

`R `^theta*``^phi*` `^phi*` `^theta = -2*G*M/(r^7*sin(theta)^2)

`R `^phi*``^t*` `^t*` `^phi = G*M/(r^4*sin(theta)^2*(2*G*M-r))

`R `^t*``^phi*` `^t*` `^phi = -G*M/(r^4*sin(theta)^2*(2*G*M-r))

`R `^phi*``^r*` `^r*` `^phi = -(2*G*M-r)*G*M/(r^6*sin(theta)^2)

`R `^r*``^phi*` `^r*` `^phi = (2*G*M-r)*G*M/(r^6*sin(theta)^2)

`R `^phi*``^theta*` `^theta*` `^phi = -2*G*M/(r^7*sin(theta)^2)

`R `^theta*``^phi*` `^theta*` `^phi = 2*G*M/(r^7*sin(theta)^2)

(4)

4*((2*G*M-r)*G*M/r^2.(G*M/(r^4*(2*G*M-r))))+4*((2*G*M-r)*G*M*sin(theta)^2/r^2.(G*M/(r^4*sin(theta)^2*(2*G*M-r))))+16*(G*M/r^3.(G*M/r^3))+4*(G*M/(2*G*M-r).((2*G*M-r)*G*M/r^6))+4*(G*M*sin(theta)^2/(2*G*M-r).((2*G*M-r)*G*M/(r^6*sin(theta)^2)))+16*(G*M*sin(theta)^2*r.(G*M/(r^7*sin(theta)^2)))