Asymptotic causality and hyperbolicity in higher curvature gravity and holography

Asymptotic causality (AC) is the requirement that signals propagating through any given spacetime do not violate the asymptotic causal structure. It is possible to classify pairs of boundary points into spacelike, timelike or null separated with respect to this prescribed asymptotic structure, and AC implies that signals propagating through the bulk cannot communicate spacelike separated points. We will prove that asymptotic causality is a necessary condition for the global hyperbolicity of a general gravitational problem.
We will also analyze some of the possible applications of this notion of causality from the point of view of higher curvature gravity in asymptotically flat space or holography. Considering higher derivative corrections to the graviton three-point coupling we may argue that these are constrained by causality. Lorentz invariance allows further structures beyond the one present in the Einstein theory. We devise a thought experiment involving a high energy scattering process which leads to causality violation if the graviton three-point vertex contains the additional structures. This violation can only be fixed by adding an infinite tower of extra massive particles with higher spins, $J>2$.