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HELP FOR: kdelta
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SYNOPSIS:
- The kdelta{^a b} object is used to represent the Kronecker delta matrix:
kdelta{^a b} := 1 if a = b,
0 otherwise.
- It can be used in grdef() to define new objects, for instance:
> grdef ( `T{^a b} := phi(t)*kdelta{^a b}` ):
- It can also be used in grdef() to select a single component of a tensor.
The component is selected by prefixing its name with a dollar sign `$',
as in:
> grdef ( `v{^a} := kdelta{ ^a $t }` ):
If the components are {r,theta,phi,t} then this command is equivalent
to
> grdef ( `v{^a} := [ 0, 0, 0, psi(t) ]` ):
however in the previous case, one would still need to run grcalc( v(up) )
to assign the components of v.
- kdelta is defined automatically and can not be calculated or displayed or
altered as other tensors.
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EXAMPLE:
> qload ( schw ):
> grdef ( `T{^a ^b} := rho(t)*kdelta{^a $t}*kdelta{^b $t}` ):
> grcalc ( T(up,up) ):
Calculated T2(up,up) for schw. (0.080000 sec.)
> grdisplay ( _ ):
For the schw spacetime:
T(up,up)
[ 0 0 0 0 ]
[ ]
a b [ 0 0 0 0 ]
T = [ ]
[ 0 0 0 0 ]
[ ]
[ 0 0 0 rho(t) ]
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SEE ALSO: grdef, grt_objects.
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