Black Hole Entropy for Two Higher Derivative Theories of Gravity

The dark energy issue is attracting the attention of an increasing number of physicists all over the world. Among the possible alternatives to explain what as been named the Mystery of the Millennium are the so-called Modified Theories of Gravity. A crucial test for such models is represented by the existence and (if this is the case) the properties of their black hole solutions. Nowadays, to our knowledge, only two non-trivial, static, spherically symmetric, solutions with vanishing cosmological constant are known by Barrow & Clifton (2005) and Deser, Sarioglu & Tekin (2008). The aim of the paper is to discuss some features of such solutions, with emphasis on their thermodynamic properties such as entropy and temperature.