Demonstration 3( statlim ): Invariant ($R_{abcd;e}R^{abcd;e}$) which vanishes on the stationary limit surface of theKerr spacetime.

> restart:

> grtw();

`GRTensorII Version 1.79 (R6)`

`2 February 2001`

`Developed by Peter Musgrave, Denis Pollney and Kay...

`Copyright 1994-2001 by the authors.`

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

`e:/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)*` d`*r^`2 `/(r^2-2*m*r+a^2)+(r^...
` ds`^2 = (r^2+u^2)*` d`*r^`2 `/(r^2-2*m*r+a^2)+(r^...

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

`The Kerr metric in Boyer-Lindquist type coordinate...

> grlib(dinvar):

`Differential Invariants`

`Last modified Jan. 20, 1995`

> grcalc(diRiem);

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

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

`CPU Time ` = .701

> grmap(_,subs,u=a*cos(theta),`x`);

Applying routine subs to diRiem

> gralter(_,2,7);

Component simplification of a GRTensorII object:

Applying routine `simplify[trig]` to object diRiem

Applying routine factor to object diRiem

`CPU Time ` = .140

> grdisplay(_);

`For the newkerr spacetime:`

` R_{a b c d ; e} R^{a b c d ; e}`

`diRiem ` = 720*(r^4-4*r^3*cos(theta)*a-6*cos(theta...
`diRiem ` = 720*(r^4-4*r^3*cos(theta)*a-6*cos(theta...

>