Demonstration 2 (rnds1): Automatic generation of an NPtetrad and calculation of the Petrov type, and Ricci scalars.

> 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(rnds);

`Default spacetime` = rnds

`For the rnds spacetime:`

Coordinates

x(up)

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

`Line element`

` ds`^2 = ` d`*r^`2 `/(1-2*m/r-1/3*Lambda*r^2+e^2/(...

`The Reissner-Nordstrom-de Sitter metric`

> nptetrad([r,t]);

The metric signature of the rnds spacetime is +2.

In order to create an NP-tetrad, the signature of g(dn,dn) will be changed to -2.

Continue? (1=yes [default], other=no) :

nptetrad> 1;

1

> grcalc(Petrov);

`Basis/tetrad related object definitions`

`Last modified 23 January 2001`

Created a definition for e(bdn,dn,pdn)

`CPU Time ` = .451

> grdisplay(_);

`For the rnds spacetime:`

`Petrov Type`

`Petrov Type ` = `D (or simpler)`

> PetrovReport();

`The conclusion 'Petrov type = D (or simpler)'`

`for the rnds metric`

`was based on the following results:`

`Weyl scalar Psi0` = 0

`Weyl scalar Psi1` = 0

`Weyl scalar Psi2 could not be evaluated to zero.`

`Weyl scalar Psi3` = 0

`Weyl scalar Psi4` = 0

`---> Therefore the metric is Petrov D (or simpler)...

`--------------------------------------------------...

`The quantities that could not be evaluated to zero...

`Weyl scalar Psi2` = (-m*r+e^2)/(r^4)

> grcalc(RicciSc);

`CPU Time ` = .20e-1

> grdisplay(_);

`For the rnds spacetime:`

`Ricci Scalar, Phi00`

Phi00 = 0

`Ricci Scalar, Phi01`

Phi01 = 0

`Ricci Scalar, Phi02`

Phi02 = 0

`Ricci Scalar, Phi11`

Phi11 = 1/2*e^2/(r^4)

`Ricci Scalar, Phi12`

Phi12 = 0

`Ricci Scalar, Phi22`

Phi22 = 0

`NPLambda := Ricci Scalar/24`

NPLambda = 1/6*Lambda

>