Black holes with a generalized gravitational action.

Microscopic black holes are sensitive to higher dimension operators in the gravitational action. We compute the influence of these operators on the Schwarzschild solution using perturbation theory. All (time reversal invariant) operators of dimension six are included (dimension four operators don’t alter the Schwarzschild solution). Corrections to the relation between the Hawking temperature and the black hole mass are found. The entropy is calculated using the Gibbons-Hawking prescription for the Euclidean path integral and using naive thermodynamic reasoning. These two methods agree, however, the entropy is not equal to 1/4 the area of the horizon. ⋆ Work supported in part by the U.S. Dept. of Energy under Contract no. DEAC-03-81ER40050. Classical black hole solutions to generalizations of Einsteins gravitational action