  We present a new analysis of Kerr-Newman-deSitter black holes in terms of
thermodynamic quantities that are defined in the observable portion of the
universe; between the black hole and cosmological horizons. In particular, we
replace the mass $m$ with a new 'area product' parameter $X$. The physical
region of parameter space is found analytically and thermodynamic quantities
are given by simple algebraic functions of these parameters. We find that
different geometrical properties of the black holes are usefully distinguished
by the sum of the black hole and cosmological entropies. The physical parameter
space breaks into a region in which the total entropy, together with $\Lambda$,
$a$ and $q$ uniquely specifies the black hole, and a region in which there is a
two-fold degeneracy. In this latter region, there are isentropic pairs of black
holes, having the same $\Lambda$, $a$, and $q$, but different $X$. The
thermodynamic volumes and masses differ in such that there are high and low
density branches. The partner spacetimes are related by a simple inversion of
$X$, which has a fixed point at the state of maximal total entropy. We compute
the compressibility at fixed total entropy and find that it diverges at the
maximal entropy point. Hence a picture emerges of high and low density phases
merging at this critical point.
