>    restart:

>    grtw(); 

Scalar invariant library.

Last modified 25 March 1997.

`Differential Invariants`

`Last modified Jan. 20, 1995`

`Basis/tetrad related object definitions`

`Last modified 23 January 2001`

`Last built 27 May, 1999`

`Last built 27 May, 1999`

`GRTensorII Version 1.79 (R4)`

`6 February 2001`

`Developed by Peter Musgrave, Denis Pollney and Kayll Lake`

`Copyright 1994-2001 by the authors.`

`Latest version available from: http://grtensor.phy.queensu.ca/`

`c:/Grtii(6)/Metrics`

>    qload(newkerr);

`Default spacetime` = newkerr

`For the newkerr spacetime:`

Coordinates

x(up)

`x `^a = vector([r, u, phi, t])

`Line element`

` ds`^2 = (r^2+u^2)/(r^2-2*m*r+a^2)*` d`*r^`2 `+(r^2+u^2)/(a^2-u^2)*` d`*u^`2 `+(a^2-u^2)/a^2*(r^2+a^2+2*(a^2-u^2)*m*r/(r^2+u^2))*` d`*phi^`2 `-4*(a^2-u^2)/a*m*r/(r^2+u^2)*` d`*phi^` `*`d `*t^` `+(-1+2...

Constraints = [u = a*cos(theta)]

`The Kerr metric in Boyer-Lindquist type coordinates (u=a*cos(theta)).`

>    grcalc(diWeyl); 

Created a definition for C(dn,dn,up,up,cdn)

`CPU Time ` = .313

>    gralter(_,13,6,7); 

Component simplification of a GRTensorII object:

Applying routine `Apply constraints repeatedly` to object diWeyl

Applying routine expand to object diWeyl

Applying routine factor to object diWeyl

`CPU Time ` = .63e-1

>    grdisplay(_);

`For the newkerr spacetime:`

` C_{a b c d ; e} C^{a b c d ; e}`

`diWeyl ` = 720*m^2*(r^4-4*r^3*a*cos(theta)-6*a^2*r^2*cos(theta)^2+4*r*a^3*cos(theta)^3+a^4*cos(theta)^4)*(r^4+4*r^3*a*cos(theta)-6*a^2*r^2*cos(theta)^2-4*r*a^3*cos(theta)^3+a^4*cos(theta)^4)*(a^2*cos(...
`diWeyl ` = 720*m^2*(r^4-4*r^3*a*cos(theta)-6*a^2*r^2*cos(theta)^2+4*r*a^3*cos(theta)^3+a^4*cos(theta)^4)*(r^4+4*r^3*a*cos(theta)-6*a^2*r^2*cos(theta)^2-4*r*a^3*cos(theta)^3+a^4*cos(theta)^4)*(a^2*cos(...

>    Aman:=-360*m^2*((r-I*a*cos(theta))^(-1)*(r+I*a*cos(theta))^(-9)+(r-I*a*cos(theta))^(-9)*(r+I*a*cos(theta))^(-1))*(r^2-2*m*r+a^2*cos(theta)^2);

Aman := -360*m^2*(1/((r-I*a*cos(theta))*(r+a*cos(theta)*I)^9)+1/((r-I*a*cos(theta))^9*(r+a*cos(theta)*I)))*(a^2*cos(theta)^2+r^2-2*m*r)

>    factor(simplify(Aman));

-720*m^2*(r^4-4*r^3*a*cos(theta)-6*a^2*r^2*cos(theta)^2+4*r*a^3*cos(theta)^3+a^4*cos(theta)^4)*(r^4+4*r^3*a*cos(theta)-6*a^2*r^2*cos(theta)^2-4*r*a^3*cos(theta)^3+a^4*cos(theta)^4)*(a^2*cos(theta)^2+r^...
-720*m^2*(r^4-4*r^3*a*cos(theta)-6*a^2*r^2*cos(theta)^2+4*r*a^3*cos(theta)^3+a^4*cos(theta)^4)*(r^4+4*r^3*a*cos(theta)-6*a^2*r^2*cos(theta)^2-4*r*a^3*cos(theta)^3+a^4*cos(theta)^4)*(a^2*cos(theta)^2+r^...

>    simplify(%+grcomponent(diWeyl,[]));

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