A No Black Hole Theorem
  We show that one cannot put a stationary (extended) black hole inside certain gravitating flux-tubes. This includes an electric flux-tube in five-dimensional Einstein-Maxwell theory, as well as the standard flux-branes of string theory. The flux always causes the black hole to grow indefinitely. One finds a similar restriction in a Kaluza-Klein setting where the higher dimensional spacetime contains no matter. 
Gavin S. Hartnett, Gary T. Horowitz, and Kengo Maeda
hep-th gr-qc