EFFECTIVE POTENTIAL OF A BLACK-HOLE IN THERMAL-EQUILIBRIUM WITH QUANTUM-FIELDS

Expectation values of one-loop renormalized thermal equilibrium stress -energy tensors of free conformal scalars, spin-1/2 fermions, and U(1) gauge fields on a Schwarzschild black hole background are used as sou rces in the semiclassical Einstein equation. The back reaction and new equilibrium metric have been found at O(hBAR) for each spin field in previous work. In this paper, the nature of the modified black hole sp acetime is explored through calculations of the effective potential fo r null and timelike orbits. Significant novel features affecting the m otions of both massive and massless test particles show up at lowest o rder in epsilon=(M(Pl)/M)2 < 1, where M is the black hole mass, and M( Pl) is the Planck mass. Specifically, we find an increase in the black hole capture cross sections, and the existence of a region near the b lack hole with a repulsive contribution, generated by the U(1) back re action, to the gravitational force. There is no such effect for other spins. Extrapolating our results suggests a tendency towards the forma tion of stable circular orbits, but the result cannot be established i n O(hBAR): the change in the metric becomes large and it changes its s ignature. We also consider the back reaction arising from multiple fie lds, which ultimately should be useful for treating a black hole in eq uilibrium with field ensembles belonging to gauge theories. In certain circumstances, however, reliable results will require calculations be yond O(hBAR).