We construct a class of counterexamples to cosmic censorship in four
dimensional Einstein-Born-Infeld theory with asymptotically anti-de Sitter
boundary conditions, and investigate the effect of the Born-Infeld parameter
b in comparison with the counterpart of Einstein-Maxwell theory. When a
charged massive scalar field is included into the action, we find that this
class of counterexamples to cosmic censorship would be removed if the charge of
scalar fields is above the minimum value of charge qmin​. In particular,
the minimum value of charge required to preserve cosmic censorship increases
with the increasing of Born-Infeld parameter. Meanwhile, we also show the lower
bounds on charge-to-mass ratio with the different values of Born-Infeld
parameter.Comment: 14 pages, 9 figure