  We calculate quantum gravitational corrections to the entropy of black holes
using the Wald entropy formula within an effective field theory approach to
quantum gravity. The corrections to the entropy are calculated to second order
in curvature and we calculate a subset of those at third order. We show that,
at third order in curvature, interesting issues appear that had not been
considered previously in the literature. The fact that the Schwarzschild metric
receives corrections at this order in the curvature expansion has important
implications for the entropy calculation. Indeed, the horizon radius and the
temperature receive corrections. These corrections need to be carefully
considered when calculating the Wald entropy.
