  In this work, the interaction of electromagnetic fields with a rotating
(Kerr) black hole is explored in the context of Born-Infeld (BI) theory of
electromagnetism instead of standard Maxwell theory and particularly BI theory
versions of the four horizon boundary conditions of Znajek and Damour are
derived. Naturally, an issue to be addressed is then whether they would change
from the ones given in Maxwell theory context and if they would, how.
Interestingly enough, as long as one employs the same local null tetrad frame
as the one adopted in the works by Damour and by Znajek to read out physical
values of electromagnetic fields and fictitious surface charge and currents on
the horizon, it turns out that one ends up with exactly the same four horizon
boundary conditions despite the shift of the electrodynamics theory from a
linear Maxwell one to a highly non-linear BI one. Close inspection reveals that
this curious and unexpected result can be attributed to the fact that the
concrete structure of BI equations happens to be such that it is
indistinguishable at the horizon to a local observer, say, in Damour's local
tetrad frame from that of standard Maxwell theory.
