Non-local equation of state in general relativistic radiating spheres

We show that under particular circumstances a general relativistic spherica lly symmetric bounded distribution of matter could satisfy a non-local equa tion of state. This equation describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that po int, but as a functional throughout the enclosed configuration. We have fou nd that these types of dynamic bounded matter configurations, with constant compactness or gravitational potentials at the surface, admit a conformal Killing vector field and fulfil the energy conditions for anisotropic imper fect fluids. We present several analytical and numerical models satisfying these equations of state which collapse as reasonable radiating anisotropic spheres in general relativity.