> restart: grtw();

`GRTensorII Version 1.80-pre2 (R6)`

`2 March 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`

Coordinate calculation

> qload(visser);

`Default spacetime` = visser

`For the visser spacetime:`

Coordinates*`:`*x(up)

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

`Spacetime signature`*`:`*sig

`Signature ` = 2

`Line element`*`:`*ds

` ds`^2 = -exp(A1(r))*` d`*t^`2 `+exp(B1(r))*` d`*r...

Constraints = [A1(r) = int(2*epsilon*sqrt(-x*diff(z...

> grcalc(G(up,dn));

Created definition for G(up,dn) 

`CPU Time ` = .230

> gralter(_,13,2,7);

Component simplification of a GRTensorII object:

Applying routine `Apply constraints repeatedly` to object G(up,dn)

Applying routine `simplify[trig]` to object G(up,dn)

Applying routine factor to object G(up,dn)

`CPU Time ` = .140

> grdisplay(_);

`For the visser spacetime:`

`G(up,dn)`*`:`*G(up,dn)

`G `^t*``[t] = exp(int((-epsilon*sqrt(-x*diff(z(x),...
`G `^t*``[t] = exp(int((-epsilon*sqrt(-x*diff(z(x),...

`G `^r*``[r] = exp(int((-epsilon*sqrt(-x*diff(z(x),...

`G `^theta*``[theta] = exp(int((-epsilon*sqrt(-x*di...

`G `^phi*``[phi] = exp(int((-epsilon*sqrt(-x*diff(z...

Basis calculation

> qload(visserb);

`Default spacetime` = visserb

`For the visserb spacetime:`

Coordinates*`:`*x(up)

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

`Spacetime signature`*`:`*sig

`Signature ` = 2

`Basis inner product`*`:`*eta(bup,bup)

eta^`(a)`*``^`(b)` = matrix([[-1, 0, 0, 0], [0, 1, ...

`Basis (covariant components)`*`:`*w1(dn)

omega1[a] = vector([exp(1/2*A1(r)), 0, 0, 0])

`Basis (covariant components)`*`:`*w2(dn)

omega2[a] = vector([0, exp(1/2*B1(r)), 0, 0])

`Basis (covariant components)`*`:`*w3(dn)

omega3[a] = vector([0, 0, exp(1/2*B1(r))*r, 0])

`Basis (covariant components)`*`:`*w4(dn)

omega4[a] = vector([0, 0, 0, exp(1/2*B1(r))*r*sin(t...

Constraints = [A1(r) = int(2*epsilon*sqrt(-x*diff(z...

> grcalc(G(bdn,bdn));

Created definition for rot(bdn,bup,bdn) 

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

`CPU Time ` = .220

> gralter(_,13,2,7);

Component simplification of a GRTensorII object:

Applying routine `Apply constraints repeatedly` to object G(bdn,bdn)

Applying routine `simplify[trig]` to object G(bdn,bdn)

Applying routine factor to object G(bdn,bdn)

`CPU Time ` = .60e-1

> grdisplay(_);

`For the visserb spacetime:`

`Covariant Einstein`*`:`*G(bdn,bdn)

G[``(`1`)*``(`1`)] = -exp(int((-epsilon*sqrt(-x*dif...
G[``(`1`)*``(`1`)] = -exp(int((-epsilon*sqrt(-x*dif...

G[``(`2`)*``(`2`)] = exp(int((-epsilon*sqrt(-x*diff...

G[``(`3`)*``(`3`)] = exp(int((-epsilon*sqrt(-x*diff...

G[``(`4`)*``(`4`)] = exp(int((-epsilon*sqrt(-x*diff...

>