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 non-zero logarithmic correction to the area-entropy relation, would also imply a modification of the area-mass relation for quantum black holes.Comment: 3 page

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom