=============================================================================== HELP FOR: kdelta =============================================================================== 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. ------------------------------------------------------------------------------- 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) ] ------------------------------------------------------------------------------- SEE ALSO: grdef, grt_objects. ===============================================================================