Nonlocal Equation of State in Anisotropic Static Fluid Spheres in General Relativity

We present a general method for obtaining static anisotropic spherically symmetric solutions, starting from known density profiles and satisfying a nonlocal equation of state. This equation of state describes, at a given point, the components of the corresponding energymomentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. In order to establish the physical acceptability of the proposed static family of solutions satisfying nonlocal equation of state, we study the consequences imposed by the junction and energy conditions on bounded matter distributions. We work out several examples from known density profiles and show that general relativistic anisotropic spherical compact objects could satisfy this type of equation of state.