  The formation of horizons in finite time according to distant observers
results in a number of remarkable properties of the objects they bound. Subject
to this requirement, spherically-symmetric black holes can only decrease in
mass, while white holes can only expand. We provide a detailed analysis of the
latter scenario, focussing on the energy-momentum tensor near the horizon and
the experiences of various observers. Kerr-Vaidya metrics are the simplest
dynamical axially-symmetric solutions, all of which violate the null energy
condition and thus are not excluded by the criterion of finite formation time.
Of the four classes of Kerr-Vaidya metrics, two correspond to the allowed
spherically-symmetric solutions: evaporating black holes and expanding white
holes. We demonstrate a consistent description of accreting black holes based
on the ingoing Kerr-Vaidya metric with increasing mass, and show that the model
can be extended to cases where the angular momentum to mass ratio varies. Their
apparent horizon is shown to be weakly singular. Pathologies are also
identified in the evaporating white hole geometry which reinforce controversies
arising from the classical and quantum instabilities of their static
counterparts. We also describe a generalization of the equivalence between
Rindler and Schwarzschild horizons to Kerr-Vaidya black holes, and describe the
relevant geometric constructions.
