  The aim of this article is to calculate (to first order in $\hbar$) the
renormalized effective action of a self interacting massive scalar field
propagating in the space-time due to a cylindrically symmetric, rotating body.
The vacuum (exterior space-time) contribution is model independent, we also
consider the simplest case of a core (interior space-time) model, namely a
cylindrical shell. The heat kernel of the system is calculated, and used to
obtain an expression for the determinant of the Klein-Gordon operator on the
space-time manifold. New ultra-violet poles are discovered, and regularization
techniques are then employed to render finite the Klein-Gordon determinant and
consequently extract the regularized one loop effective action for a self
interacting scalar field theory. The coupling constants of the theory are then
renormalized. As a test case a conical singularity with non-zero flux is also
considered.
