It is argued that the Hawking radiation from black holes is not produced by the spacetime curvature as in Hawking's often repeated description (1975). Two-dimensional examples are given where the particle creation can be shown to be directly due to the collapsing object, the presence (or not) of spacetime curvature being irrelevant. A four-dimensional electrostatic example is used to show that particle creation by static external fields requires there to be no static vacuum state in the presence of the external field. A stable static vacuum does, however, exist around static black holes.