Causality bounds chaos in geodesic motion

Predictability is grounded by causality while may be practically restricted the occurrence of chaos. To reveal relation between these two popular notions, we study chaos in geodesic motion generic curved spacetimes with external potentials, where controlled a scalar potential. We develop reparametrization-independent method to analytically estimate Lyapunov exponent $\ensuremath{\lambda}$ particle motion. show that gives universal upper bound $\ensuremath{\lambda}\ensuremath{\propto}E\text{ }(E\ensuremath{\rightarrow}\ensuremath{\infty})$, which coincides energy proposed Murata, Tanahashi, Watanabe, and one authors (K. H.). also find discovered Maldacena, Shenker, Stanford can violated particular even causality. Our estimates, although waiting for numerical confirmation, hidden nature physical theories: bounds