Where is the PdV term in the fist law of black hole thermodynamics
Traditional treatments of the first law of black hole thermodynamic 
s do not 
include a discussion of pressure and volume. We give an overview of re 
cent 
developments proposing a definition of volume that can be used to ex 
tend 
the first law to include these appropriately. New results are also pre 
senting 
relating to the critical point and the associated second order phas 
e transition 
for a rotating black-hole in four-dimensional space-time which is asy 
mptot- 
ically anti-de Sitter. In line with known results for a non-rotating cha 
rged 
black-hole, this phase transition is shown to be of Van der Waals type 
with 
mean field exponents