  Kerr-Vaidya metrics are the simplest nonstationary extensions of the Kerr
metric. We explore their properties and compare them with the near-horizon
limits of the spherically symmetric self-consistent solutions (the ingoing
Vaidya metric with decreasing mass and the outgoing Vaidya metric with
increasing mass) for the evaporating and accreting physical black holes. The
Newman-Janis transformation relates the corresponding Vaidya and Kerr-Vaidya
metrics. For nonzero angular momentum, the energy-momentum tensor violates the
null energy condition (NEC). However, we show that its structure differs from
the standard form of the NEC-violating tensors. The apparent horizon in the
outgoing Kerr-Vaidya metric coincides with that of the Kerr black hole. For the
ingoing metric, its location is different. We derive the ordinary differential
equation for this surface and locate it numerically. A spherically symmetric
accreting black hole leads to a firewall -- a divergent energy density,
pressure, and flux as perceived by an infalling observer. We show that this is
also true for the outgoing Kerr-Vaidya metric
