Znajek-Damour Horizon Boundary Conditions with Born-Infeld Electrodynamics

TL;DR

This paper investigates electromagnetic interactions with rotating black holes using Born-Infeld theory, finding that horizon boundary conditions remain unchanged from Maxwell theory when using a specific local tetrad frame.

Contribution

It derives Born-Infeld versions of horizon boundary conditions and shows they are identical to Maxwell's, revealing invariance at the horizon despite non-linear electrodynamics.

Findings

Horizon boundary conditions are unchanged in BI theory compared to Maxwell.

The structure of BI equations appears indistinguishable from Maxwell at the horizon.

The result depends on the choice of local tetrad frame.

Abstract

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.