  For purposes of quantization, classical gravity is normally expressed by
canonical variables, namely the metric $g_{ab}(x)$ and the momentum
$\pi^{cd}(x)$. Canonical quantization requires a proper promotion of these
classical variables to quantum operators, which, according to Dirac, the
favored operators should be those arising from classical variables that formed
Cartesian coordinates; sadly, in this case, that is not possible. However, an
affine quantization features promoting the metric $g_{ab}(x)$ and the momentric
$\pi^c_d(x)\;[\equiv \pi^{ce}(x) \,g_{de}(x)]$ to operators. Instead of these
classical variables belonging to a constant zero curvature space (i.e., instead
of a flat space), they belong to a space of constant negative curvatures. This
feature may even have its appearance in black holes, which could strongly point
toward an affine quantization approach to quantize gravity.
