  Fluctuations around a non-trivial solution of Born-Infeld theory have a
limiting speed given not by the Einstein metric but the Boillat metric. The
Boillat metric is S-duality invariant and conformal to the open string metric.
It also governs the propagation of scalars and spinors in Born-Infeld theory.
We discuss the potential clash between causality determined by the closed
string and open string light cones and find that the latter never lie outside
the former. Both cones touch along the principal null directions of the
background Born-Infeld field. We consider black hole solutions in situations in
which the distinction between bulk and brane is not sharp such as space filling
branes and find that the location of the event horizon and the thermodynamic
properties do not depend on whether one uses the closed or open string metric.
Analogous statements hold in the more general context of non-linear
electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld
action to second order might be obtained from higher-curvature gravity in
Kaluza-Klein theory. Finally we point out some intriguing analogies with
Einstein-Schr\"odinger theory.
