  We construct a general relativistic conservation law for linear and angular
momentum for matter and gravitational fields in a finite volume of space that
does not rely on any spacetime symmetries. This work builds on our previous
construction of a general relativistic energy conservation law with the same
features. Our approach uses the Brown and York quasilocal
stress-energy-momentum tensor for matter and gravitational fields, plus the
concept of a rigid quasilocal frame (RQF) introduced in previous work. The RQF
approach allows us to construct, in a generic spacetime, frames of reference
whose boundaries are rigid (their shape and size do not change with time), and
that have precisely the same six arbitrary time-dependent degrees of freedom as
the accelerating and tumbling rigid frames we are familiar with in Newtonian
mechanics. These RQFs, in turn, give rise to a completely general conservation
law for the six components of momentum (three linear and three angular) of a
finite system of matter and gravitational fields. We compare in detail this
quasilocal RQF approach to constructing conservation laws with the usual local
one based on spacetime symmetries, and discuss the shortcomings of the latter.
These RQF conservation laws lead to a deeper understanding of physics in the
form of simple, exact, operational definitions of gravitational energy and
momentum fluxes, which in turn reveal, for the first time, the exact, detailed
mechanisms of gravitational energy and momentum transfer taking place in a wide
variety of physical phenomena, including a simple falling apple. As a concrete
example, we derive a general relativistic version of Archimedes' law that we
apply to understand electrostatic weight and buoyant force in the context of a
Reissner-Nordstrom black hole.
