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 do not 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 ¼ the area of the horizon.

• Received 1 February 1993

DOI:https://doi.org/10.1103/PhysRevD.47.R3095