It is just for simplicity to call
a four-momemtum.
is not defined (general, nor even Lorentz) covariantly nor as
a volume integral of tensor density of weight
. The integrand
is a tensor density of weight
. In
Section 6.1, we will find that
equals
in a certain sense.
is an energy of the star (modulo the
contribution from the integrand
) if the star considered were isolated, the space-time is asymptotically flat,
and finally, if we integrate over a spacelike hypersurface, rather than integrate only over the body zone of the
star [115].