Znajek-Damour horizon boundary conditions with Born-Infeld electrodynamics- art. no. 104024

In this work, the interaction of electromagnetic fields with a rotating (Ke rr) black hole is explored in the context of the Born-Infeld (BI) theory of electromagnetism instead of standard Maxwell theory and particularly BI th eory 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 the Maxwell theory context and if they do, h ow. Interestingly enough, as long as one employs the same local null tetrad frame as the one adopted in the works of Damour and of Znajek to read out physical values of electromagnetic fields and a fictitious surface charge a nd currents on the horizon, it turns out that one ends up with exactly the same four horizon boundary conditions despite the shift of the electrodynam ics theory from a linear Maxwell one to a highly nonlinear BI one. Close in spection 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 Da mour's local tetrad frame from that of standard Maxwell theory.