Mode-sum prescription for renormalized expectation values for a charged quantum scalar field on a charged black hole

We present a new mode-sum prescription for the efficient computation of renormalized expectation values for a massive, charged, quantum scalar field propagating on a curved space-time background. Our method is applicable to any static, spherically symmetric, four-dimensional space-time with a time-independent, background electrostatic potential and can be used to find the renormalized scalar condensate, current and stress-energy tensor. As an explicit example, we present a calculation of these quantities for a charged scalar field in the Hartle-Hawking state on a Reissner-Nordström black hole background.