  We demonstrate that the emergence of a curved spacetime ``effective
Lorentzian geometry'' is a common and generic result of linearizing a field
theory around some non-trivial background. This investigation is motivated by
considering the large number of ``analog models'' of general relativity that
have recently been developed based on condensed matter physics, and asking
whether there is something more fundamental going on. Indeed, linearization of
a classical field theory (a field theoretic ``normal mode analysis'') results
in fluctuations whose propagation is governed by a Lorentzian-signature curved
spacetime ``effective metric''. For a single scalar field, this procedure
results in a unique effective metric, which is quite sufficient for simulating
kinematic aspects of general relativity (up to and including Hawking
radiation). Quantizing the linearized fluctuations, the one-loop effective
action contains a term proportional to the Einstein--Hilbert action, suggesting
that while classical physics is responsible for generating an ``effective
geometry'', quantum physics can be argued to induce an ``effective dynamics''.
The situation is strongly reminiscent of Sakharov's ``induced gravity''
scenario, and suggests that Einstein gravity is an emergent low-energy
long-distance phenomenon that is insensitive to the details of the high-energy
short-distance physics. (We mean this in the same sense that hydrodynamics is a
long-distance emergent phenomenon, many of whose predictions are insensitive to
the short-distance cutoff implicit in molecular dynamics.)
