The Ernst spacetime is a solution of the Einstein-Maxwell equations de
scribing two charged black holes accelerating apart in a uniform elect
ric (or magnetic) field. As the field approaches a critical value, the
black hole horizon appears to touch the acceleration horizon. We show
that weak cosmic censorship cannot be violated by increasing the fiel
d past this critical value: The event horizon remains intact.-On the o
ther hand, strong cosmic censorship does appear to be violated in this
spacetime: For a certain range of parameters, we find evidence that t
he inner horizon is classically stable.