  Horava-Witten spacetimes necessarily include two branes of opposite tension.
If these branes are BPS we are led to a puzzle: a negative tension brane should
be unstable as it can loose energy by expanding, whereas a BPS brane should be
stable as it resides at a minimum of the energy. We provide a detailed analysis
of the energy of such braneworld spacetimes in 5 dimensions. This allows us to
show by a non-perturbative positive energy theorem that Horava-Witten
spacetimes are stable, essentially because the dynamics of the branes is
entirely accounted for by the behaviour of the bulk fields. We also perform an
ADM perturbative Hamiltonian analysis at quadratic order in order to illustrate
the stability properties more explicitly.
