  Einstein's field equations with a background source term that induces
perturbations and the applications of this new formalism to a compact dense
matter relativistic star are presented. We introduce a new response kernel in
the field equations between the metric and fluid perturbations. A source term
which drives or induces the sub-hydro mesoscopic scales perturbations in the
astrophysical system, is of importance here. Deterministic as well as
stochastic perturbations for the radial case are worked out as solutions of
field equations. We also touch upon polar perturbations that are deterministic
with oscillatory parts. The stochastic perturbation are of significance in
terms of two point or point separated correlations which form the building
blocks for studying equilibrium and non-equilibrium statistical mechanics for
the system. Our main aim is to build a theory for intermediate scale physics,
for dense exotic matter and investigate structure of the compact astrophysical
objects. Specifically, turbulence which connects various scales in superfluid
matter in the dense stars is an area gaining importance. The work presented
here is the starting point for new theoretical frame work that touches upon
various yet unexplored scales where mechanical and dynamical effects interior
to the matter of the star are of significance. Thus there is scope for
extending studies in asteroseismology to mesoscopic effects at the new
intermediate scales in the cold dense matter fluid . This is expected to enable
us to probe astrophysical features at refined scales through theoretical
formulations as well as for observational consequences.
