Semiclassical Quadratic Gravity and Black Hole Thermodynamics

The thermodynamical interpretation of black holes proposed for the first time by Gibbons and Hawking [1–3] has completely renewed our understanding of this type of solution. First, within such interpretation, black holes appear to have a mutual interaction with the surrounding environment and are, therefore, truly physical objects. Second, the derivation of the thermodynamical properties of black holes is the first robust result of a semiclassical approach to gravity. It is semiclassical in two distinct senses: the original derivation of Hawking radiation is semiclassical in the sense that the gravitational interaction is considered purely classical but the matter (or radiation) fields populating this classical spacetime have quantum nature; it is also semiclassical in the sense that all the thermodynamical properties of black holes can be derived from the mean field approximation of a consistently defined quantum theory of gravity. The two interpretations are, in any case, complementary and consistent one with the other.