Coulomb Scalars, Tendicities, and Vorticities of Black Hole Spacetimes in Numerical Relativity

A choice of time slicing specifies a split of the Weyl tensor into gravitoelectric and gravitomagnetic components. These components can be combined into a single complex quantity, one of whose eigenvalues gives an invariant called the Coulomb scalar; or they can be treated as separate real quantities, whose respective eigenvalues have been termed the tendicity and vorticity. This latter pair has recently gained attention as a vehicle for visualization and analysis of strongly curved spacetimes, and here we compare Coulomb-scalar and tendicity-vorticity calculations for black holes in binary systems.