Abstract. 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 non-zero logarithmic correction to the area–entropy relation would also imply a modification of the area–mass relation for quantum black holes.

PACS number: 04.70.Dy

Print publication: Issue 14 (21 July 2004)
Received 30 May 2004
Published 23 June 2004