  Conservation laws have many applications in numerical relativity. However, it
is not straightforward to define local conservation laws for general dynamic
spacetimes due the lack of coordinate translation symmetries. In flat space,
the rate of change of energy-momentum within a finite spacelike volume is
equivalent to the flux integrated over the surface of this volume; for general
spacetimes it is necessary to include a volume integral of a source term
arising from spacetime curvature. In this work a study of continuity of matter
in general relativity is extended to include angular momentum of matter and
Noether currents associated with gauge symmetries. Expressions for the Noether
charge and flux of complex scalar fields and complex Proca fields are found
using this formalism. Expressions for the angular momentum density, flux and
source are also derived which are then applied to a numerical relativity
collision of boson stars in 3D with non-zero impact parameter as an
illustration of the methods.
