Black holes are thermodynamical objects. They are characterized by an internal energy (mass), a temperature, an entropy, …

The entropy, for instance has a nice geometric connection, since it is given by a quarter of horizon area !

In the presence of a cosmological constant, the thermodynamical phase space can be enlarged, including a cosmological pressure. In this context, one can introduce equations of state relating pressure to volume, temperature and so on.

It was recently suggested that an exact black hole analogue of Van der Waals fluid, i.e. fluid with an intermolecular interaction and a size of the fluid constituents, can be devised in 4D.

In a recent paper, I’ve extended the 4D solution to arbitrary number of dimensions and various horizon topology of the horizon. This could be useful in the AdS/CFT context.

http://arxiv.org/abs/arXiv:1411.7850