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The spherically symmetric, static spacetime generated by a cross-flow of non-interacting null dust streams can be conveniently interpreted as the radiation atmosphere of a star, which also receives exterior radiation. Formally, such a superposition of sources is equivalent to an anisotropic fluid. Therefore, there is a preferred time function in the system, defined by this reference fluid. This internal time is employed as a canonical coordinate, in order to linearize the Hamiltonian constraint. This turns to be helpful in the canonical quantization of the geometry of the radiating atmosphere.

CANONICAL ANALYSIS OF RADIATING ATMOSPHERES OF STARS IN EQUILIBRIUM