  We study the effective geometry felt by the fluctuations of open strings
living on the worldvolume of probe D-branes in the presence of background
electromagnetic fields. This is captured by an effective action consisting of a
Maxwell term and a topological term, with the role of the metric played by the
open string metric. Studying generalized Eddington-Finkelstein coordinates for
stationary but non-static manifolds, we consider an open string membrane
paradigm to obtain a generic formula for the DC transport coefficients,
including the effect of external electromagnetic fields present on the
worldvolume of the probe branes. We show that the previously studied singular
shell, present when a critical electric field strength is turned on, behaves as
a horizon for the open string degrees of freedom. The results of this analysis
can be used to define a membrane paradigm for a very general class of
spacetimes with non-diagonal metrics.
