Hadamard renormalization of the stress energy tensor in a spherically symmetric black hole space-time with an application to lukewarm black holes

We consider a quantum field which is in a Hartle-Hawking state propagating in a spherically symmetric black hole space-time. We calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, in the exterior region of this space-time. We then specialize these results to the case of the "lukewarm'' Riessner-Nordstrom-de Sitter black hole.