Thermodynamical universality of the Lovelock black holes

The necessary and sufficient condition for the thermodynamical universality of the static spherically symmetric Lovelock black hole is that it is the Nth order pure Lovelock I >-vacuum solution. By universality we mean the thermodynamical parameters: temperature and entropy always bear the same relation to the horizon radius for d = 2N + 1, 2N + 2 dimensions for all N which is the degree of the Lovelock polynomial. For instance, the entropy always goes in terms of the horizon radius as r (h) and r (h) (2) , respectively for the odd and even dimensions. Not only that the universality uniquely identifies the pure Lovelock black hole with I >, it is the characterizing property of this class of black holes.