  In this article, I discuss the construction of some globally conserved
currents that one can construct in the absence of a Killing vector. One is
based on the Komar current, which is constructed from an arbitrary vector field
and has an identically vanishing divergence. I obtain some expressions for
Komar currents constructed from some generalizations of Killing vectors which
may in principle be constructed in a generic spacetime. I then present an
explicit example for an outgoing Vaidya spacetime which demonstrates that the
resulting Komar currents can yield conserved quantities that behave in a manner
expected for the energy contained in the outgoing radiation. Finally, I
describe a method for constructing another class of (non-Komar) globally
conserved currents using a scalar test field that satisfies an inhomogeneous
wave equation, and discuss two examples; the first example may provide a useful
framework for examining the arrow of time and its relationship to energy
conditions, and the second yields (with appropriate initial conditions) a
globally conserved energy- and momentumlike quantity that measures the degree
to which a given spacetime deviates from symmetry.
