Script started on Mon May 9 20:47:52 2011
Octopus 1 % maple
|\^/| Maple 9 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2003
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> readlib(grii):
> grtensor():
GRTensorII Version 1.79 (R4)
6 February 2001
Developed by Peter Musgrave, Denis Pollney and Kayll Lake
Copyright 1994-2001 by the authors.
Latest version available from: http://grtensor.phy.queensu.ca/
Defaults read from the local grtensor.ini
> makeg(sphere);
Makeg 2.0: GRTensor metric/basis entry utility
To quit makeg, type 'exit' at any prompt.
Do you wish to enter a 1) metric [g(dn,dn)],
2) line element [ds],
3) non-holonomic basis [e(1)...e(n)], or
4) NP tetrad [l,n,m,mbar]?
makeg>3;
Enter coordinates as a LIST (eg. [t,r,theta,phi]):
makeg>[theta,phi];
Would you like to enter 1) covariant components,
2) contravariant components, or
3) both.
makeg>1;
Enter the covariant components of basis vector '1' as a LIST (eg. [1,0,0,0])
or differential (eg. d[x] + d[y]):
makeg>r*d[theta];
Enter the covariant components of basis vector '2' as a LIST (eg. [1,0,0,0])
or differential (eg. d[x] + d[y]):
makeg>r*sin(theta)*d[phi];
Is the basis inner product 1) Diagonal, or
2) Symmetric?
makeg>1;
Enter eta[1,1]:
makeg>1;
Enter eta[2,2]:
makeg>1;
If there are any complex valued coordinates, constants or functions
for this spacetime, please enter them as a SET ( eg. { z, psi } ).
Complex quantities [default={}]:
makeg>;
{}
The values you have entered are:
Coordinates = [theta, phi]
Basis 1-forms:
omega[1] = [r, 0]
omega[2] = [0, r sin(theta)]
Inner product of basis vectors:
[1 0]
eta = [ ]
[0 1]
You may choose to 0) Use the metric WITHOUT saving it,
1) Save the metric as it is,
2) Re-enter a basis vector,
3) Re-enter the inner product,
4) Add/change constraints,
5) Add a text description, or
6) Abandon this metric and return to Maple.
makeg>0;
Default spacetime = sphere
For the sphere spacetime:
Coordinates
x(up)
a
x = [theta, phi]
Basis inner product
eta(bup, bup)
(a) (b) [1 0]
eta = [ ]
[0 1]
Basis 1-forms
e(bdn, dn)
[r 0 ]
e [(a)] [b] = [ ]
[0 r sin(theta)]
makeg() completed.
> grcalc(metric):grdisplay(metric);
For the sphere spacetime:
Covariant metric tensor
g(dn, dn)
[ 2 ]
[r 0 ]
g [a] [b] = [ ]
[ 2 2]
[0 r sin(theta) ]
> grcalc(rot(bup,bdn,bdn)):grdisplay(rot(bup,bdn,bdn));
Created definition for rot(bup,bdn,bdn)
Created a definition for e(bdn,dn,pdn)
For the sphere spacetime:
rot(bup,bdn,bdn)
(2) cos(theta)
gamma [ (1) (2)] = ------------
r sin(theta)
(1) cos(theta)
gamma [ (2) (2)] = - ------------
r sin(theta)
> grcalc(R(bup,bdn,bdn,bdn)):grdisplay(R(bup,bdn,bdn,bdn));
For the sphere spacetime:
R(bup,bdn,bdn,bdn)
(1) 1
R [ (2) (1) (2)] = ----
2
r
(2) 1
R [ (1) (1) (2)] = - ----
2
r
> quit;
Octopus 2 % exit
Script done on Mon May 9 20:50:03 2011