> 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(statica);

`Default spacetime` = statica

`For the statica spacetime:`

Coordinates

x(up)

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

`Line element`

` ds`^2 = a(r)*` d`*r^`2 `+r^2*` d`*theta^`2 `+r^2*...

> grcalc(G(dn,dn));

`CPU Time ` = .50e-1

> dsolve(grcomponent(G(dn,dn),[t,t])+Lambda*grcomponent(g(dn,dn),[t,t])=0,a(r));

a(r) = -3*r/(-3*r+r^3*Lambda-3*_C1)

The standard notation for the constant is -2*m

> a(r):=r/(r-r^3*Lambda/3-2*m);

a(r) := r/(r-1/3*r^3*Lambda-2*m)

> dsolve(grcomponent(G(dn,dn),[r,r])+Lambda*grcomponent(g(dn,dn),[r,r])=0,b(r));

b(r) = _C1*(-3*r+r^3*Lambda+6*m)/r

Scale t so that the constant is 1

> b(r):=-(-r+r^3*Lambda/3+2*m)/r;

b(r) := -(-r+1/3*r^3*Lambda+2*m)/r

> grdisplay(g(dn,dn));

`For the statica spacetime:`

`Covariant metric tensor`

g(dn,dn)

`g `[a]*``[b] = matrix([[r/(r-1/3*r^3*Lambda-2*m), ...

>