Feynman Green function inside a Schwarzschild black hole

A representation is given for the Feynman Green function corresponding to a scalar field that propagates in Schwarzschild spacetime and which is subject to the Hartle-Hawking boundary conditions. This representation is valid for all values of the Schwarzschild radial coordinate r and is used to obtain an expression for 〈${\mathrm{cphi}}^2$ ${〉}_{\mathrm{reg}}$ for the region interior to the horizon. This expression is evaluated numerically for the range 0.5M<r<2M.