Dj. Loranz et al., THERMAL DIVERGENCES ON THE EVENT HORIZONS OF 2-DIMENSIONAL BLACK-HOLES, Physical review. D. Particles and fields, 52(8), 1995, pp. 4554-4558
The expectation value of the stress-energy tenser [T-mu upsilon] of a
free conformally invariant scalar field is computed in a general stati
c two-dimensional black hole spacetime when the held is in either a ze
ro temperature vacuum state or a thermal state at a nonzero temperatur
e. It is found that for every static two-dimensional black hole the st
ress-energy diverges strongly on the event horizon unless the held is
in a state at the natural black hole temperature which is defined by t
he surface gravity of the event horizon. This implies that both extrem
e and nonextreme two-dimensional black holes can only be in equilibriu
m with radiation at the natural black hole temperature.