I'm just learning to use the ccgrg package for computing Riemann curvatures etc in Mathematica. The package has most of the useful geometric tensors as built-in functions, but I can't find a function for obtaining the Hodge dual of a tensor, or equivalently the Levi-Civita tensor. Is there one?
Mathematica itself has a function LeviCivitaTensor[d] built in, but it uses the indices in a different manner than ccgrg (and seems to be the Levi-Civita symbol rather than the tensor as it misses the $\sqrt{|g|}$ that is required of a general-coordinate tensor). Converting the way the entries are referenced looks rather indirect and inelegent.
Any suggestions?
Added comment: I think I have found a nasty bug in the ccgrg package. I tried computing $R^{ijmn}R_{ijmn}$ for the Kerr metric by evaluating
Sum[tRiemannR[i,j,m,n]tRiemannR[-i,-j,-m,-n]
,{i,dim},{j,dim},{m,dim},{n,dim}]
as illustrated in the documentation in arXiv:1603.05819 eq 11.
It did not get the correct answer. With the ccgrg convention, the indices are summed frm 1 to 4. I noticed that the incorrect answer no longer depended on the mass parameter $m$ however. A bit of digging shows that $m$ was everywhere replaced by the number 4. It seems that the way they re-implement the mathematica "Sum" function replaces the $m$ in the expressions with the last value (here 4) of the dummy summation index $m$ in "Sum". i.e. the summation variables are not private to the subroutine that uses them. This is a bit off-putting. I don't think that the regular Sum[expression, {m,1,4}]
does this.