Demonstration 1(br):Definition of the Bel-Robinson Tensor and check of identities in the Kerr-Newman metric.

> restart:

> grtw();

> qload(newkn);

> grdef(`T{(c d e f)}:=C{a c d b}*C{^a e f^b}+Cstar{a c d b}*Cstar{^a e f^b}`);

Created definition for C(up,dn,dn,up)

Created definition for Cstar(up,dn,dn,up)

Created definition for T(dn,dn,dn,dn)

> grdef(`TT{c d}:=T{^a a c d}`);

Created definition for T(up,dn,dn,dn)

Created definition for TT(dn,dn)

> grdef(`TC{b c d}:=T{^a b c d ;a}`);

Created a definition for T(up,dn,dn,dn,cdn)

Created definition for TC(dn,dn,dn)

> grcalc(T(dn,dn,dn,dn));

> gralter(_,expand,factor);

Component simplification of a GRTensorII object:

Applying routine expand to object T(dn,dn,dn,dn)

Applying routine factor to object T(dn,dn,dn,dn)

Check that $T^{a}_{~acd}=0$.

> grcalc(TT(dn,dn));

> grdisplay(_);

Check that $T^{abcd}_{~~~~;a}=0$ for vacuum ($Q=0$).

> Q:=0;

> grcalc(TC(dn,dn,dn));

> gralter(_,expand,factor);

Component simplification of a GRTensorII object:

Applying routine expand to object TC(dn,dn,dn)

Applying routine factor to object TC(dn,dn,dn)

> grdisplay(_);

Display $T_{abcd}$ for the Kerr metric

> grmap(T(dn,dn,dn,dn),subs,u=a*cos(theta),`x`);

Applying routine subs to T(dn,dn,dn,dn)

> grdisplay(_);

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