  We present SphericalNR, a new framework for the publicly available Einstein
Toolkit that numerically solves the Einstein field equations coupled to the
equations of general relativistic magnetohydrodynamics (GRMHD) in a 3+1 split
of spacetime in spherical coordinates without symmetry assumptions. The
spacetime evolution is performed using reference-metric versions of either the
Baumgarte-Shapiro-Shibata-Nakamura equations or the fully covariant and
conformal Z4 system with constraint damping. We have developed a
reference-metric version of the Valencia formulation of GRMHD with a vector
potential method, guaranteeing the absence of magnetic monopoles during the
evolution. In our framework, every dynamical field (both spacetime and matter)
is evolved using its components in an orthonormal basis with respect to the
spherical reference-metric. Furthermore, all geometric information about the
spherical coordinate system is encoded in source terms appearing in the
evolution equations. This allows for the straightforward extension of Cartesian
high-resolution shock-capturing finite volume codes to use spherical
coordinates with our framework. To this end, we have adapted GRHydro, a
Cartesian finite volume GRMHD code already available in the Einstein Toolkit,
to use spherical coordinates. We present the full evolution equations of the
framework, as well as details of its implementation in the Einstein Toolkit. We
validate SphericalNR by demonstrating it passes a variety of challenging code
tests in static and dynamical spacetimes.
