  In this paper we report on what we believe is the first successful
implementation of relativistic hydrodynamics, coupled to dynamical spacetimes,
in spherical polar coordinates without symmetry assumptions. We employ a
high-resolution shock-capturing scheme, which requires that the equations be
cast in flux-conservative form. One example of such a form is the :Valencia"
formulation, which has been adopted in numerous applications, in particular in
Cartesian coordinates. Here we generalize this formulation to allow for a
reference-metric approach, which provides a natural framework for calculations
in curvilinear coordinates. In spherical polar coordinates, for example, it
allows for an analytical treatment of the singular r and sin(\theta) terms that
appear in the equations. We experiment with different versions of our
generalized Valencia formulation in numerical implementations of relativistic
hydrodynamics for both fixed and dynamical spacetimes. We consider a number of
different tests -- non-rotating and rotating relativistic stars, as well as
gravitational collapse to a black hole -- to demonstrate that our formulation
provides a promising approach to performing fully relativistic astrophysics
simulations in spherical polar coordinates.
