  We argue that an arbitrary general relativistic static anisotropic fluid
sphere, (static and spherically symmetric but with transverse pressure not
equal to radial pressure), can nevertheless be successfully mimicked by
suitable linear combinations of theoretically attractive and quite simple
classical matter: a classical (charged) isotropic perfect fluid, a classical
electromagnetic field, and a classical (minimally coupled) scalar field. While
the most general decomposition is not unique, a preferred minimal decomposition
can be constructed that is unique. We show how the classical energy conditions
for the anisotropic fluid sphere can be related to energy conditions for the
isotropic perfect fluid, electromagnetic field, and scalar field components of
the model. Furthermore we show how this decomposition relates to the
distribution of both electric charge density and scalar charge density
throughout the model. The generalized TOV equation implies that the perfect
fluid component in this model is automatically in internal equilibrium, with
pressure forces, electric forces, and scalar forces balancing the gravitational
pseudo-force. Consequently, we can build theoretically attractive matter models
that can be used to mimic almost any static spherically symmetric spacetime.
