  Black hole initial data is usually produced using Bowen-York type puncture
initial data or by applying an excision boundary condition. The benefits of the
Bowen-York initial data are the ability to specify the spin and momentum of the
system as parameters of the initial data. In an attempt to extend these
benefits to other formulations of the Einstein constraints, the puncture method
is reformulated using distributions as source terms. It is shown how the
Bowen-York puncture black hole initial data and the trumpet variation is
generated by distributional sources. A heuristic argument is presented to argue
that these sources are the general sources of spin and momentum. In order to
clarify the meaning of other distributional sources, an exact family of initial
data with generalized sources to the Hamiltonian constraint are studied;
spinning trumpet black hole initial data and black hole initial data with
higher order momentum sources are also studied.
