Critical behavior for the dilaton black holes Original Research Article

We study the critical behavior in the black p-branes and four-dimensional charged dilaton black holes. We calculate the thermodynamic fluctuations in the various (microcanonical, canonical, and grandcanonical) ensembles. It is found that the extremal limit of some black configurations has a critical point and a phase transition takes place from the extremal to non-extremal black configurations. Some critical exponents are obtained, which satisfy the scaling laws. This is related to the fact that the entropy of these black configurations is a homogeneous function.