Theoretical Background

While the tensor components evolved in an ADM-style evolution of Einstein's equations are adequate carriers of the geometrical information which defines the spacetime, they are not directly amenable to providing an interpretation of the geometrical content. The fundumental trouble is that the tensor components are not coordinate independent, the value of each component (for a non-vanishing tensor) can vary arbitrarily with coordinate change. PsiKadelia calculates several more geometrically defined quantities. The complex valued Weyl scalars, $\Psi_0$,$\Psi_1$,$\Psi_2$,$\Psi_3$,$\Psi_4$ are coordinate independent, but do depend on a choice of tetrad (an orthonormal complex basis for the tangent space of the spacetime). The tetrad is defined in relation to the numerical grid coordinates, but the resulting $\Psi$'s are less sensitive to coordinate freedom. PsiKadelia also calculates two genuinely coordinate invariant quantities, $I$ and $J$. For more background see [40] and [41].