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HELP FOR: grconstraint
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CALLING SEQUENCE: grconstraint ( metric ):
PARAMETERS: metric - the name of a previously loaded metric
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SYNOPSIS:
- GRTensorII allows the specification of constraint equations that must be
satisfied by functions in the metric or basis.
- Constraint equations may be added to a spacetime, removed or re-arranged
using this command. grconstraint() is menu driven and prompts for
addition/modification/deletion of constraint equations.
- Constraints can be applied to an object calculated from a metric or basis
by using gralter().
- Constraints specified using grconstraint() can be saved with the metric
file using grsaveg().
- Constraints may also be specified by makeg(), and will be loaded
automatically as the spacetime is loaded.
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EXAMPLE:
# In the following example, the bondi metric is loaded and the constraints
# m(r,v) = M, and c(r,v) = C
# are specified. The Ricci tensor is calculated for the metric in terms
# of the general functions m(r,v) and c(r,v), and the constraints are then
# applied to show that the Ricci tensor is zero when these functions are
# constants.
> qload ( bondi ):
> grconstraint ( bondi ):
Constraint specification and manipulation
Do you wish to
1) Add a constraint to the metric
2) Remove a constraint from the metric
3) Modify a metric constraint
4) Display the existing constraints
5) Exit
Enter 1-5 > 1
Please enter the new constraint as an equation (of the form
f(x,y) = g(x) + h(y), for example):
Enter equation : m(r,v) = M
The new constraint equation is :
m(r, v) = M
Constraint specification and manipulation
Do you wish to
1) Add a constraint to the metric
2) Remove a constraint from the metric
3) Modify a metric constraint
4) Display the existing constraints
5) Exit
Enter 1-5 > 1
Please enter the new constraint as an equation (of the form
f(x,y) = g(x) + h(y), for example):
Enter equation : c(r,v) = C
The new constraint equation is :
c(r, v) = C
Constraint specification and manipulation
Do you wish to
1) Add a constraint to the metric
2) Remove a constraint from the metric
3) Modify a metric constraint
4) Display the existing constraints
5) Exit
Enter 1-5 > 4
For the bondi spacetime:
constraints
constraint = [m(r, v) = M, c(r, v) = C]
Constraint specification and manipulation
Do you wish to
1) Add a constraint to the metric
2) Remove a constraint from the metric
3) Modify a metric constraint
4) Display the existing constraints
5) Exit
Enter 1-5 > 5
> grcalc ( R(dn,dn) ):
> grdisplay ( R(dn,dn) ):
For the bondi spacetime:
Covariant Ricci
d
---- c(r, v)
dr
R [r] [r] = 2 ------------
c(r, v) r
.
.
.
etc.
> gralter ( R(dn,dn) );
Component Alteration of a grtensor object:
(use ?name for help on a particular simplification routine)
Choose which routine to apply:
0) none
1) simplify() try all simplification techniques
2) simplify[trig] apply trig simplification
3) simplify[power] simplify powers, exp and ln
4) simplify[hypergeom] simplify hypergeometric functions
5) simplify[radical] convert radicals,log,exp to canonical form
6) expand()
7) factor()
8) normal()
9) sort()
10) simplify[sqrt,symbolic] allows sqrt(r^2) = r
11) simplify[trigsin] trig simp biased to sin
12) Apply constraints
13) Apply constraints repeatedly
14) other user specified routine
Number of routine to apply > 12;
Applying routine Apply constraints to object R(dn,dn)
> grdisplay ( R(dn,dn) );
For the bondi spacetime:
Covariant Ricci
R(dn,dn) = All components are zero
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SEE ALSO: makeg, gralter, grsaveg.
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