There are two types of fundamental quantum gravitational mass amplitude states that are denoted by the subscripts D and P. The D amplitudes lead to Einstein's usual general relativity mass density functions. The P amplitudes lead to Einstein's additional pressure mass densities, 3P/c². Both of these densities appear in the stress energy momentum tensor of general relativity. Here they appear as solutions to a non-linear Schrödinger equation and carry three quantising parameters (l_D,m) and (l_P,m), The l_D,l_P values are subsets of the usual electronic quantum variable l which is here denoted by l' to avoid confusion. The m parameter is exactly the same as the electronic quantum theory m, there the z component of angular momentum. In this paper, these parametric relations are briefly displayed followed by an account of the connection to the spherical harmonic functions symmetry system that is necessarily involved. Taken together, the two types of mass density can be integrated over configuration space to give quantised general relativity galactic masses in the form of cosmological mass spectra as was shown in previous papers. Here this aspect has been extended to ensure that every galaxy component of the spectra has a quantised black hole core with a consequent quantised surface area. This is achieved by replacing the original free core radius parameter r_ε with the appropriate Schwarzschild radius associated with the core mass. Explanations are given for the choices of two further, originally free, parameters, t_b, θ₀. The main result from this paper is a quantum classification scheme for galaxies determined by the form of their dark matter spherical geometry.