Central equation of state in spherical characteristic evolutions

We study the evolution of a perfect-fluid sphere coupled to a scalar radiation field. By ensuring a Ricci invariant regularity as a conformally flat spacetime at the central world line we find that the fluid coupled to the scalar field satisfies the equation of state ${\rho }_c+3p_c=\mathrm{\text{const}}$ at the center of the sphere, where the energy ${\rho }_c$ density and the pressure $p_c$ do not necessarily contain the scalar field contribution. The fluid can be interpreted as anisotropic and radiant because of the scalar field, but it becomes perfect and nonradiative at the center of the sphere. These results are currently being considered to build up a numerical relativistic hydrodynamic solver.