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

TL;DR

This paper investigates graviton propagation near small black holes in Einstein-Gauss-Bonnet theory, revealing conditions for negative time delay and discussing implications for causality and black hole physics.

Contribution

It extends previous work on graviton time delay by analyzing smooth black hole spacetimes and introduces a speed limit for small black holes in this theory.

Findings

Gravitons can experience time advance near small black holes.

Deflection angles less than π indicate repulsive gravity at short distances.

Small black holes cannot be boosted to near-light speeds, limiting time machine constructions.

Abstract

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