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Expectation values of one-loop renormalized thermal equilibrium stress-energytensors of free conformal scalars, spin-${1 \over 2}$ fermions and U(1) gaugefields on a Schwarzschild black hole background are used as sources in thesemi-classical Einstein equation. The back-reaction and new equilibrium metricare solved for at $O({\hbar})$ for each spin field. The nature of the modifiedblack hole spacetime is revealed through calculations of the effectivepotential for null and timelike orbits. Significant novel features affectingthe motions of both massive and massless test particles show up at lowest orderin $\epsilon= (M_{Pl}/M)^2 < 1$, where $M$ is the renormalized black hole mass,and $M_{Pl}$ is the Planck mass. Specifically, we find the tendency for\underline{stable} circular photon orbits, an increase in the black holecapture cross sections, and the existence of a gravitationally repulsive regionassociated with the black hole which is generated from the U(1) back-reaction.We also consider the back-reaction arising from multiple fields, which will beuseful for treating a black hole in thermal equilibrium with field ensemblesbelonging to gauge theories.Comment: 25 pages (not including seven figures), VAND-TH-93-6. Typed in Latex,  uses RevTex macro

Effective potential of a black hole in thermal equilibrium with quantum fields