  We discuss the fundamentals of classical black hole (BH) thermodynamics in a
new framework determined by light surfaces and their frequencies. This new
approach allows us to study BH transitions inside the Kerr geometry. In the
case of BHs, we introduce a new parametrization of the metric in terms of the
maximum extractable rotational energy or, correspondingly, the irreducible
mass, which is an alternative to the spin parametrization.
  It turns out that BH spacetimes with spins $a/M= \sqrt {8/9}$ and
$a/M=1/\sqrt{2}$ show anomalies in the rotational energy extraction and surface
gravity whereas the case $a/M=\sqrt{3}/2$ is of particular relevance to study
the variations of the horizon area. We find the general conditions under which
BH transitions can occur and express them in terms of the masses of the initial
and final states. This shows that BH transitions in the Kerr geometry are not
arbitrary but depend on the relationship between the mass and spin of the
initial and final states. From an observational point of view, we argue that
near the BH poles it is possible to detect photon orbits with frequencies that
characterize the light surfaces analyzed in this work.
