  We consider a self-gravitating system containing a globally timelike Killing
vector and a nonlinear Born-Infeld electromagnetic field and scalar fields. We
prove that under certain boundary conditions (asymptotically flat/AdS) there
can't be any nontrivial field configurations in the spacetime. To explore
nontrivial solutions one should break any of the conditions we imposed. The
case with another type of nonlinear electromagnetic field is also analyzed, and
similar conclusions have been obtained under certain conditions.
