Consistency between Bulk and Boundary Causalities in Asymptotically Anti-de Sitter Spacetimes

We investigate the consistency between bulk and boundary causalities in static, spherically symmetric, asymptotically anti-de Sitter (AdS) spacetimes. We derive a general formula that provides sufficient conditions for time advance, where bulk propagation arrives earlier than any boundary propagation. As an application, we show that in Reissner–Nordström–anti de Sitter spacetime, no geodesic satisfies the sufficient conditions for time advance even in the super-extremal case. Furthermore, we demonstrate that the Einstein–Euler–Heisenberg theory exhibits time advance when one or a linear combination of the coupling constants is positive and below an upper bound determined by the AdS length scale.