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.