  Finsler spacetimes have become increasingly popular within the theoretical
physics community over the last two decades. Because physicists need to use
pseudo-Finsler structures to describe propagation}of signals, there will be
nonzero null vectors in both the tangent and cotangent spaces --- this causes
significant problems in that many of the mathematical results normally obtained
for "usual" (Euclidean signature) Finsler structures either do not apply, or
require significant modifications to their formulation and/or proof. We shall
first provide a few basic definitions, explicitly demonstrating the
interpretation of bi-metric theories in terms of pseudo-Finsler norms. We shall
then discuss the tricky issues that arise when trying to construct an
appropriate pseudo-Finsler metric appropriate to bi-metric spacetimes. Whereas
in Euclidian signature the construction of the Finsler metric typically fails
at the zero vector, in Lorentzian signature the Finsler metric is typically
ill-defined on the entire null cone.
