Causality bounds from charged shockwaves in 5d

Effective field theories are constrained by the requirement that their constituents never move superluminally on non-trivial backgrounds. In this paper, we study time delays experienced by photons propagating on charged shockwave backgrounds in five dimensions. In the absence of gravity -- where the shockwaves are electric fields sourced by boosted charges -- we derive positivity bounds for the four-derivative corrections to electromagnetism, reproducing previous results derived from scattering amplitudes. By considering the gravitational shockwaves sourced by Reissner-Nordstr\"om black holes, we derive new constraints in the presence of gravity. We observe the by-now familiar weakening of positivity bounds in the presence of gravity, but without the logarithmic divergences present in 4d. We find that the strongest bounds appear by examining the time delay near the horizon of the smallest possible black hole, and discuss on the validity of the EFT expansion in this region. We comment on our bounds in the context of the swampland program as well as their relation with the positivity bounds obtained from dispersion relations.