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Camanho, Edelstein, Maldacena and Zhiboedov have shown that gravitons canexperience a negative Shapiro time delay, i.e. a time advance, inEinstein-Gauss-Bonnet theory. They studied gravitons propagating in singular"shock-wave" geometries. We study this effect for gravitons propagating insmooth black hole spacetimes. For a small enough black hole, we find thatgravitons of appropriate polarisation, and small impact parameter, canexperience time advance. Such gravitons can also exhibit a deflection angleless than $\pi$, characteristic of a repulsive short-distance gravitationalinteraction. We discuss problems with the suggestion that the time advance canbe used to build a "time machine". In particular, we argue that a small blackhole cannot be boosted to a speed arbitrarily close to the speed of light, aswould be required in such a construction.

Graviton time delay and a speed limit for small black holes in Einstein-Gauss-Bonnet theory