Canonical Analysis of Radiating Atmospheres of Stars in Equilibrium

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.