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. The quantum theory of gravitational collapse motivated many authors to study models with both in-and outgoing thin null dust shells in a spherically symmetric geometry. Such models can equally apply for other phenomena, like radiative domains around stars in thermodynamical equilibrium. The model of a radiative stellar atmosphere composed of two null dust streams provides good prospects for carrying out a complete canonical analysis and quantization. We present here an overview of the Hamiltonian description of two cross-streaming radiation fields with spherical symmetry and the first steps towards the Dirac quantization of this constrained Hamiltonian system. Letelier demonstrated that the energy-momentum tensor of two superimposed, counter-propagating radiation fields is equivalent to the energy-momentum tensor of a specific anisotropic fluid. 1 Based on this algebraic equivalence we have recently shown that the dynamics derived by extremizing the matter Lagrangians of these two models are the same. 2 For the purpose of canonical analysis the two cross-flowing radiation fields can therefore be substituted with a single anisotropic fluid (with radial pressure equaling the energy density and no tangential pressures). The equivalence with the fluid model is crucial for our purposes since earlier works on the Hamiltonian formalism of two cross-flowing radiation fields with spherical symmetric geometry, although achieving important results, could not solve the problem of the absence of an internal time. 3 The possibility of replacing the two