Static Anisotropic Solutions to Einstein Equations with a Nonlocal Equation of State

We present a general method to obtain static anisotropic spherically symmetric solutions, satisfying a nonlocal equation of state, from known density profiles. This equation of state describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. In order to establish the physical aceptability of the proposed static family of solutions satisfying nonlocal equation of state,$$we study the consequences imposed by the junction and energy conditions for anisotropic fluids in bounded matter distribution. It is shown that a general relativistic spherically symmetric bounded distributions of matter, at least for certain regions, could satisfy a nonlocal equation of state.