  The kinematics of the stellar halo hold important clues to the assembly
history and mass distribution of the Galaxy. In this study, we map the
kinematics of stars across the Galactic halo with the H3 Survey. We find a
complex distribution that breaks both azimuthal symmetry about the $Z$-axis and
mirror symmetry about the Galactic plane. This asymmetry manifests as large
variations in the radial velocity dispersion $\sigma_r$ from as ``cold'' as 70
$\text{km}\text{ s}^{-1}$ to as ``hot'' as 160 $\text{km}\text{ s}^{-1}$. We
use stellar chemistry to distinguish accreted stars from in-situ stars in the
halo, and find that the accreted population has higher $\sigma_r$ and radially
biased orbits, while the in-situ population has lower $\sigma_r$ and isotropic
orbits. As a result, the Galactic halo kinematics are highly heterogeneous and
poorly approximated as being spherical or axisymmetric. We measure radial
profiles of $\sigma_r$ and the anisotropy parameter $\beta$ over Galactocentric
radii $10-80\text{ kpc}$, and find that discrepancies in the literature are due
to the nonspherical geometry and heterogeneous nature of the halo.
Investigating the effect of strongly asymmetric $\sigma_r$ and $\beta$ on
equilibrium models is a path forward to accurately constraining the Galactic
gravitational field, including its total mass.
