Demonstration 1 (bondi): The Bondi metric.

> 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`

> grOptionDisplayLimit:=9000;

grOptionDisplayLimit := 9000

> qload(bondig1);

`Default spacetime` = bondig1

`For the bondig1 spacetime:`

Coordinates

x(up)

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

`Line element`

` ds`^2 = (-v(u,r,theta)*exp(2*b(u,r,theta))/r+w(u,...
` ds`^2 = (-v(u,r,theta)*exp(2*b(u,r,theta))/r+w(u,...

`The Bondi Metric `

> grcalcalter(detg,g(up,up),R(dn,dn,dn,dn),R(dn,dn),Ricciscalar,G(dn,dn),expand);

Simplification will be applied during calculation.

Applying routine expand to object detg

Applying routine expand to object g(up,up)

Applying routine expand to object g(dn,dn,pdn)

Applying routine expand to object Chr(dn,dn,dn)

Applying routine expand to object R(dn,dn,dn,dn)

Applying routine expand to object Chr(dn,dn,up)

Applying routine expand to object R(dn,dn)

Applying routine expand to object tRicciscalar

Applying routine expand to object G(dn,dn)

`CPU Time ` = .141

> grmap(_,autoAlias,`x`);

Applying routine autoAlias to detg

Applying routine autoAlias to g(up,up)

Applying routine autoAlias to R(dn,dn,dn,dn)

Warning, alias or macro v[r] defined in terms of v

Warning, alias or macro b[r] defined in terms of b

Warning, alias or macro w[r] defined in terms of w

Warning, alias or macro y[r] defined in terms of y

Applying routine autoAlias to R(dn,dn)

Applying routine autoAlias to Ricciscalar

Applying routine autoAlias to G(dn,dn)

To display the rather long output do grdisplay(_);

grdisplay(_);