Is the horizon of an eternal black hole really smooth?

We point out that in many eternal black holes, including a Schwarzschild eternal black hole and an eternal black hole in $AdS_5$, instant folded strings are created in the past wedge and render the region just outside the horizon singular. We also make a conjecture regarding instant folded D-branes and discuss their possible implications for eternal black holes. In particular, we argue that the bulk modes responsible for Poincare recurrence, when it occurs in the dual quantum field theory, are either instant folded strings or instant folded D-branes.