Geometrodynamics in a spherically symmetric, static crossflow of null dust

The spherically symmetric, static spacetime generated by a crossflow of non-interacting radiation streams, treated in the geometrical optics limit (null dust) is equivalent to an anisotropic fluid forming a radiation atmosphere of a star. This reference fluid provides a preferred / internal time, which is employed as a canonical coordinate. Among the advantages we encounter a new Hamiltonian constraint, which becomes linear in the momentum conjugate to the internal time (therefore yielding a functional Schr\"{o}dinger equation after quantization), and a strongly commuting algebra of the new constraints.