High-order corrections to the entropy and area of quantum black holes

The celebrated area-entropy formula for black holes has provided the most important clue in the search for the elusive theory of quantum gravity. We explore the possibility that the (linear) area-entropy relation acquires some smaller corrections. Using the Boltzmann-Einstein formula, we rule out the possibility for a power-law correction and provide severe constraints on the coefficient of a possible log-area correction. We argue that a nonzero logarithmic correction to the area-entropy relation would also imply a modification of the area-mass relation for quantum black holes.