A method to compute〈φ2〉in asymptotically flat, static, spherically symmetric spacetimes

A method is presented which allows for the computation of $〈{\phi }^2〉$ for scalar fields at zero and nonzero temperatures in asymptotically flat, static, spherically symmetric spacetimes. If a spacetime has event horizons, the method works in the region exterior to the outermost event horizon. The method is used to compute $〈{\phi }^2〉$ for massless and massive scalar fields in Reissner-Nordström and extreme Reissner-Nordström spacetimes.